MINISTRY OF REGIONAL
DEVELOPMENT AND TOURISM
GOVERNMENT OF ROMANIA
www.mdrt.ro
1. ------IND- 2011 0655 RO- EN- ------ 20120103 --- --- PROJET
ORDER
No.... of.....
for the approval of the technical regulation
“Guidelines for the calculation and construction of timber-concrete composite floors for
old and new buildings”, code GP 116-2011
In accordance with the provisions of Article 10 and Article 38(2) of Law No
10/1995 regarding quality in constructions, with its subsequent modifications, the provisions
of Article 2(3) and (4) of the Rules regarding the types of technical regulations and costs for
the regulatory activity in the field of constructions, town planning, landscaping, and habitat,
approved by Government Decision No 203/2003, with its subsequent modifications and
supplementation, and the provisions of Government Decision No 1016/2004 regarding
measures for organising and carrying out the exchange of information in the field of technical
standards and regulations, as well as the rules regarding information society services between
Romania and the EU Member States, as well as the European Commission, with its
subsequent modifications,
taking into consideration the Approval Report No 19 of 2 June 2011 of the Specialist
Technical Committee No 5 “Structures for constructionsˮ,
on the grounds of Article 5(II)(e) and Article13(6) of Government Decision No
1631/2009 concerning the organisation and operation of the Ministry of Regional
Development and Tourism, with its subsequent modifications and supplementation,
the Ministry of Regional Development and Tourism hereby issues the following
ORDER:
Article 1.-The technical regulation “Guidelines for the calculation and construction
of timber-concrete composite floors for old and new buildings, Code GP 116-2011, drawn up
by the “URBAN-INCERCˮ National Institute for Research and Development in the field of
Constructions, Town Planning, and Sustainable Territorial Development, Timisoara branch,
stipulated in the annex*) that is an integrated part of the present order, is hereby approved.
Article 2. - The present order shall be published in the Official Journal of Romania,
Part I and shall come into force 30 days after its date of publication.
This technical regulation was adopted in accordance with procedure No............ of ................
stipulated by Directive 98/34/EC of the European Parliament and of the Council of 22 June
1998, laying down a procedure for the provision of information in the field of technical
standards and regulations, published in the Official Journal of the European Communities L
204 of 21 July 1998, amended by Directive 98/48/EC of 20 July 1998 of the European
Parliament and the Council, published in the Official Journal of the European Communities L
217 of 5 August 1998.
MINISTER
Elena Gabriela UDREA
________________________________________________________________________________________
* The order and its annex shall be published in the Construction Journal edited by “URBAN-INCERC,” the
National Institute for Research and Development in the field of Construction, Town Planning and Sustainable
Territorial Development, which is coordinated by the Ministry of Regional Development and Tourism.
GUIDELINES FOR THE CALCULATION AND
CONSTRUCTION OF TIMBER-CONCRETE
COMPOSITE FLOORS FOR OLD AND NEW
BUILDINGS
Code GP 116-2011
2
CONTENTS
1
GENERAL PROVISIONS
1.1
Scope
1.2
Field of application
1.3
Reference documents
1.4
Terminology
1.5
Notations
2 MAIN ELEMENTS IN THE CONSTRUCTION OF TIMBER-CONCRETE
COMPOSITE FLOORS
2.1
Timber-concrete connection
2.1.1 Theoretical aspects
2.1.2 Types of connectors
2.1.3 Timber-concrete connection stiffness
2.2
Materials
2.2.1 Concrete
2.2.2 Wood
2.2.3 Reinforcements
2.2.4 Timber-concrete connectors
3 DESIGN OF TIMBER-CONCRETE COMPOSITE FLOORS
3.1
Loads and stresses
3.2
Calculation of the connection width of the slab
3.3
General hypotheses
3.4
Calculation at the ultimate limit state and the serviceability limit state
3.4.1 Characteristics of the composite section
3.4.2 Distance between connectors
3.4.3 Verification of efforts in the composite section at the ultimate limit state in the
initial stage
3.4.4 Verification of efforts in the composite section at the ultimate limit state in the
final stage
3.4.5 Verification at the serviceability limit state in the initial stage
3.4.6 Verification at the serviceability limit state in the final stage
3.4.7 Verification of the composite floor in the areas of negative bending moment
4 CONSTRUCTIVE PROVISIONS
4.1
Dimensions
4.2
Reinforcement
4.3
Connectors
4.4
Support
4.5
Operability (serviceability)
5 BEHAVIOUR OVER TIME
6 EXECUTION PROVISIONS AND TECHNOLOGY
6.1
Provisions for new buildings
6.2
Provisions for existing buildings
ANNEX A SHEAR TESTING USING TEST SPECIMENS
General aspects
Shear testing using test specimens
Carrying out experimental tests
Determination of the load-bearing capacity and modulus of sliding
ANNEX B CALCULATION EXAMPLES
3
1
GENERAL PROVISIONS
1.1 Scope
(1)
The present guidelines refer to the calculation and construction of timberconcrete composite floors for common buildings belonging to the normal class of importance,
in accordance with the provisions
P 100-1;
(2)
The present guidelines refer to:
a. the calculation and construction of timber-concrete composite floors for new
buildings with masonry load-bearing walls;
b. possibilities and methods for refurbishing old wooden floors in existing buildings
with masonry load-bearing walls by replacing them with timber-concrete composite floors
using the existing wooden beams;
(3)
The guidelines contain provisions for ensuring the appropriate operating
behaviour, as well as the strength conditions associated with the specific limit states;
(4)
The main components of a timber-concrete composite floor are:
a.
beams made of solid wood or glued laminated timber;
b.
reinforced concrete slab cast on the upper part of the wooden beams;
c.
connector which joins the concrete slab and the wooden beams.
concrete slab
connector
wooden beams
Fig. 1–1 Principle construction of a timber-concrete composite floor
1.2 Field of application
(1)
The provisions of the guidelines shall be applied during the design and
consolidation of civilian buildings which bear mainly static loads, evenly distributed and
concentrated, applied to the upper part of the composite floor;
(2)
The guidelines shall not be applicable to the refurbishment/consolidation of
existing floors in buildings that have been declared historical monuments;
(3)
The provisions of these guidelines refer to the calculation of timber-concrete
composite floors in which the concrete slab and the wooden beams are connected by means of
semi-rigid connectors (such as cylindrical rods).
(4)
If the timber-concrete composite floors are subjected to planar stresses (seismic
or wind action), the floor must meet the horizontal washer requirements, in accordance with
the regulations in force;
(5)
The provisions of the present guidelines are addressed to technical experts,
design engineers, contractors and beneficiaries (users) of construction structures, as well as
inspection, approval, and control bodies and construction works managers;
(6)
The maximum ambient temperature at which unprotected wooden elements can
be used as part of a timber-concrete composite floor is 55C;
(7)
If laying a timber-concrete composite floor in existing buildings, the entire
building must be surveyed in order to check the strength and stability conditions, in
accordance with the provisions of the standards and regulations in force.
4
(8)
The actions, groups, and their combinations taken into consideration when
designing timber-concrete composite floors shall be established in accordance with the SR EN
1991 standards;
(9)
Timber-concrete composite floors can be made as simply supported or
continuous elements. The method of reinforcement, the way in which continuity is ensured
near the middle support for continuous elements, as well as the recommendations regarding
the construction of these types of floors are given in Chapter 4;
(10) The operating class of the wooden elements in new buildings is 1 and 2, in
accordance with SR EN 1995-1-1;
(11) The provisions of the present guidelines shall be enforced in accordance with
the technical regulations and laws in force regarding fire safety, the protection of wooden
elements against aggressive agents, and sound insulation.
1.3 Reference documents
Item
Standards
No
1
SR EN 1990-2004
2
SR EN
1990:2004/NA:2006
3
SR EN 1991-1-1-2004
4
5
6
7
8
9
10
11
SR EN 1991-1-1-2004/NA2006
SR EN 1991-1-2-2004
SR EN 1991-1-2-2004/NA2006
SR EN 1992-1-1-2004
SR EN 1992-1-1-2004/AC2008
SR EN 1992-1-1-2004/NB2008
SR EN 1995-1-1-2004
16
17
18
SR EN 1995-1-1-2004/A12008
SR EN 1995-1-1-2004/AC2006
SR EN 1995-1-1-2004/NB2008
SR EN 206-1:2002
SR EN 2061:2002/A1:2005
SR EN 206-1:2002/A2:2005
SR EN 12620+A1:2008
SR EN 409:2009
19
SR EN 26891:2002
20
SR EN 335-1:2007
12
13
14
15
Name
Eurocode: Basis of structural design
Eurocode: Basis of structural design. National Annex.
Eurocode 1: Actions on structures. Part 1-1 General actions. Densities,
self-weight, and imposed loads for buildings
Eurocode 1: Actions on structures. Part 1-1 General actions - Densities,
self-weight, operating loads for buildings. National Annex.
Eurocode 1: Actions on structures. Part 1-2 General actions. Actions on
structures exposed to fire
Eurocode 1: Actions on structures. Part 1-2 General actions. Actions on
structures exposed to fire. National Annex.
Eurocode 2: Design of concrete structures. Part 1-1 General rules and
rules for buildings
Eurocode 2: Design of concrete structures. Part 1-1 General rules and
rules for buildings
Eurocode 2: Design of concrete structures. Part 1-1 General rules and
rules for buildings. National Annex
Eurocode 5: Design of timber structures. Part 1-1: General. Common
rules and rules for buildings
Eurocode 5: Design of timber structures. Part 1-1: General. Common
rules and rules for buildings
Eurocode 5: Design of timber structures. Part 1-1: General. Common
rules and rules for buildings
Eurocode 5: Design of timber structures. Part 1-1: General. Common
rules and rules for buildings. National Annex.
Concrete Part 1: Specification, performance, production and conformity
Concrete Part 1: Specification, performance, production, and conformity
Concrete Part 1: Specification, performance, production, and conformity
Aggregates for concrete
Timber structures. Test methods. Determination of the yield moment of
dowel type fasteners
Timber structures. Joints made with mechanical fasteners. General
principles for the determination of strength and deformation
characteristics
Durability of wood and wood-based materials. Definition of operating
5
21
SR EN 927-1:2002
22
23
24
25
26
STAS 2111-1990
STAS 1455-1980
STAS 1454-1980
STAS 1451-1980
STAS 1452-1980
classes. Part 1: General aspects
Paints and varnishes. Coating materials and coating systems for exterior
wood. Part 1: Classification and selection
Steel wire nails
Threaded wood screws. Square head screw. Dimensions
Threaded wood screws. Hexagonal screw. Dimensions
Threaded wood screws. Slotted button head screw. Dimensions
Threaded wood screws. Slotted countersunk screw. Dimensions
Item
Publication
Legislative documents
No
1
Design code. Part 1-Design provisions for Order No 1711/2006 of the Ministry of Transport,
Construction and Tourism, published in the Official
buildings, Code P 100-1/2006.
Journal of Romania, Part I bis, No 803/25
September 2006, with its subsequent modifications
and supplementation
2
Seismic design code. Part III. Provisions for the Order No 704/2009 of the Ministry of Regional
seismic assessment of existing buildings, Code P Development and Housing, published in the
Official Journal of Romania, Part I bis, No 674/1
100-3/2008.
October 2009
3
Design code. Structural design fundamentals for Order No 2.230/2005 of the Ministry of Transport,
Constructions and Tourism, published in the
constructions, Code CR 0-2005.
Official Journal of Romania, Part I bis, No 148/16
February 2006, with its subsequent modifications
4
Design code for masonry structures, Code CR 6- Order No 1712/2006 of the Ministry of Transport,
Constructions and Tourism, published in the
2006.
Official Journal of Romania, Part I bis, No 807/26
September 2006
5
Normative document for the production of Order No 577/2008 of 29 April 2008 of the
concrete and execution of concrete, reinforced Ministry of Development, Public Works and
concrete, and prestressed concrete works - Part 1: Housing, published in the Official Journal of
Concrete production, code NE 012/1-2007.
Romania, Part I, No 374 of 16 May 2008
6
Normative document for the production of Order No 853/2010 of 22 November 2010 of the
concrete and execution of concrete, reinforced Ministry of Regional Development and Tourism,
concrete and prestressed concrete works - Part 2: published in the Official Journal of Romania, Part
Execution of concrete works, Code NE 012/2- I, No 853 of 20 December 2010.
2010.
7
Technical regulation regarding the protection of Order No 1731/2006 of the Ministry of Transport,
wooden building elements against aggressive Constructions and Tourism, published in the
agents - performance requirements and criteria, Official Journal of Romania, Part I, No932/16
Code ST 049-2006.
November 2006
1.4 Terminology
(1)
The terms and definitions given in SR EN 1990, SR EN 1991, SR EN 1992,
and SR EN 1995 shall be used.
(2)
Connector: connects the wooden beam to the concrete slab; it is used as a joint
with steel cylindrical rods, with or without a head, which is inserted by hitting, screwing, or
pre-drilling.
6
1.5 Notations
Latin alphabet - lower case letters
a1
a2
b
bef
d
fcd
fck
fctd
fh2d
fmd
fmk
ft0d
ft0k
fuk
fvd
fvk
fyd
fyk
kdef
l
sef
smax
smin
user
uu
uy
wfin
wfin,G
wfin,Q
winst
winst,G
winst,Q
distance from the centre of gravity of the concrete section to the centre of gravity of the
composite section
distance from the centre of gravity of the wooden section to the centre of gravity of the
composite section
distance between the beams
actual connecting width of the concrete slab
diameter
design value of the compressive strength of the concrete
characteristic value of the compressive strength of concrete, measured on the cylinder after 28
days
design tensile strength of concrete
design value of the local crushing strength of the wooden element
design value of the flexural strength of wood
characteristic value of the flexural strength of wood
design value of the resistance to stretching parallel to the fibres
characteristic value of the resistance to stretching parallel to the fibres
characteristic value of the tensile strength of the connector
design value of the shear resistance
characteristic value of the shear resistance
design value of the yield strength of steel
characteristic value of the yield stress of steel
deformation factor
span, contact length
equivalent distance between connectors
maximum distance between connectors
minimum distance between connectors
deformation at the corresponding serviceability limit state Fser
ultimate deformation (sliding or rotation)
elastic limit deformation
final camber
final camber for permanent action
final camber for variable action
instantaneous final camber
instantaneous camber for permanent action
instantaneous camber for variable action
Latin alphabet - upper case letters
%G
%Q
A1
A2
Ds
E1
E2
Ecm
Ecm,fin
Emean,fin
percentage of the permanent action
percentage of the variable action
Concrete section area
Wood section area
static ductility
longitudinal modulus of elasticity of the concrete
longitudinal modulus of elasticity of the wood
modulus of elasticity of the concrete for short-term loads
final value of the modulus of elasticity of the concrete for short-term loads
mean final value of the modulus of elasticity of the wood
7
Emed=Emean
Fîd
Fser
I1
I2
K
Kser
Kser,fin
Ku
Ku,fin
MEd
Myd
Myk
Rd
Rm = Fest
Ved
mean value of the modulus of elasticity of the wood
design value of the force in the joint
force at the serviceability limit state
moment of inertia of the concrete section
moment of inertia of the wood section
modulus of sliding
modulus of sliding at the serviceability limit state
final value of the modulus of sliding at the serviceability limit state
instantaneous modulus of sliding for ultimate limit states
final value of the modulus of sliding for ultimate limit states
design bending moment
design plastic moment of the joint
characteristic plastic moment of the joint
design value of the load-bearing capacity in the joint
maximum shear force estimated by means of calculation or initial tests
design shear force
Greek letters
stiffness reduction factor for the concrete section

stiffness reduction factor for the wood section

c 
partial coefficient for concrete
partial coefficient for the properties of the material, which also takes into consideration
M
k
c1d
cd
m1d
m2d
t2d
td
max
0
1
φ(t0
0.4 
0.6 
2
model approximations and variations
characteristics value of the density of the wood
design value of the unitary compressive stress in the concrete section
design value of the stress in the compressed fibre of the concrete section
design value of the unitary tensile stress due to bending in the concrete section
design value of the unitary tensile stress due to bending in the wood section
design value of the unitary tensile stress in the wood section
design value of the stress in the stretched fibre of the concrete section
tangential stress on the centre of gravity of the composite section
coefficient for the grouping value of a variable action
coefficient for the grouping value of a permanent action
creep coefficient for concrete
displacement relating to 40 % of the maximum shear force estimated
displacement relating to 60 % of the maximum shear force estimated
MAIN ELEMENTS IN THE CONSTRUCTION OF TIMBER-CONCRETE
COMPOSITE FLOORS
2.1 Timber-concrete connection
2.1.1 Theoretical aspects
8
(1)
In the composite element, the sliding forces are transmitted through connectors
in a concentrated (point-like) way, which creates high stresses at these points and,
consequently, corresponding deformations. Therefore, timber-concrete composite elements
which are connected by means of rods do not act as a unitary section under a bending stress,
but as two sections that are elastically connected;
(2)
The calculation methods that are usually used for timber-concrete composite
floors are based on the theory of elastic connection. According to this theory, a continuous
connector with constant stiffness can be used instead of a concentrated connector;
(3)
The calculation methods take into consideration both the deformability of the
connection between the wood and the concrete, as well as the deformability of the composite
element as a whole. The stiffness of the connectors, expressed by the modulus of sliding Kser
(and Ku, respectively) is decisive for the load-bearing capacity of a composite element. The
compliance and elastic behaviour of the connector characterise the load-bearing capacity and
deformability of the composite element;
(4)
Depending on the type of connection they provide, the connectors that are
suitable for the construction of timber-concrete composite floors can be grouped into rigid
joints made by gluing, and elastic joints, which in turn can be grouped into:
a. Mechanical joints with rod-shaped connectors: nails, screws (installed in a straight
or inclined position), profiled reinforcing steel coupons; the rods shall be fixed
directly inside the wooden beams by means of several concrete “bulbsˮ created by the
concrete of the slab penetrating into the alveoli made in the wooden beams in advance;
b.
Mechanical joints with special shapes, which consist of shoe-shaped metallic
parts screwed or nailed to the wooden beam.
2.1.2 Types of connectors
(1)
The structure and operating behaviour of timber-concrete composite elements
depend on the type of connection provided between the wooden beams and the concrete slab;
(2)
In the case of a rigid connection (by gluing), the displacements between the
wood and the concrete are null, causing the element to behave like a beam with composite
section (not covered by these guidelines);
(3)
Semi-rigid (elastic) connections allow for a certain level of displacement
between the wood and the concrete, depending on its stiffness, and can be classified as
follows:
a.
with rod-type connectors: screws, steel coupons;
b.
with special connectors and parts such as: annular wedges, cleat wedges, multi
nail plates;
c.
with integrated systems: continuous connection in the form of lattice girders; a
continuous joint made of bent metal sheet; with shoe pieces;
(4)
The elements used to connect the wood and the concrete have a wide range of
configuration options, some of the significant ones being presented below;
(5)
Wood to concrete connector with cylindrical rods/concrete alveoli (Fig. 2-1.):
Oblique edges and coach screws
Spikes and coach screws
9
Vertical steel coupons bent to 90, fixed in the wooden beam
with epoxy resin in pre-drilled holes
Vertical nails on one or two rows
Ø65 holes
Ø16
reinforcement
fixed chemically
in Ø18 holes
Vertical steel coupons or dowels bent to 90, in alveoli (holes) made in the wooden beam, fixed with epoxy resin in pre-drilled
holes
Connecto
r
Concrete
PVC sheet
Wood shoring
Wooden
beam
Vertical or oblique screws positioned in one or two rows, in an alternating, crossed way
axle
support
Concrete slab
Ø8 connectors
(Pc52)
Slab
reinforcement
Wooden beam
Ø36 alveoli
Vertical reinforcing steel coupons in concrete alveoli
10
Concrete slab
Ø8 screws
Slab
reinforcement
axl
support
e
Wooden beam
Ø8 screws
Screws inclined at 45, positioned on two alternating, crossed rows
Plastic protective cap
Ø12mm nut (posttensioning)
Steel flange
Steel nut
Plastic
protective
pipe
Ø12 mm
threaded bar
Epoxy resin
Ø10 mm longitudinal
reinforcement
Stressed screws
Fig. 2–1 Timber-concrete connector with cylindrical rods/concrete alveoli
(6)
Timber-concrete connectors with special pipes and parts (Fig. 2-2)
Pipe coupons
Bolt connector
11
Multi nail plate
PVC sheet
Multi nail plates bent to 90 joined on the sides or top of the wooden beams
Fig. 2–2 Connection with metallic pipes and plates
(7)
Timber-concrete joints with integrated system connectors (Fig. 2-3)
Connection with special shoe and reinforcing steel bars
COVERING CONCRETE
REINFORCEMENT
FORM
METALLIC GIRDER
CONNECTOR
BEAMS WITH KERTRAVE SYSTEM
12
Connection made using connectors and reinforced concrete ribs
Concret
e
Reinforcement
Wooden
beam
Connector
Multi nail plate inserted in a channel made in the wooden beam
Fig. 2–3 Connection made using integrated system connectors
2.1.3 Timber-concrete connection stiffness
(1)
The stiffness of the connecting elements, expressed by the modulus of sliding
Kser (and Ku, respectively), shall be determined by means of calculation or shear tests, using
timber-concrete composite specimens, in accordance with SR EN 26891;
F
2–1
K ser  0,4 est
ν 0,4
where:
Fest – maximum shear force estimated by means of calculation or initial tests
0.4 – displacement relating to 40 % of the maximum shear force estimated
(2)
For the behaviour of the timber-concrete connection at the ultimate limit state
and the serviceability limit state to be taken into consideration in the static calculations, the
connectors should be distributed on the basis of the static ductility, in accordance with
relationship (2–2) and the connection models given in Figure 2-4:
u
2–2
DS  u
uy
13
F
a).
(a)
Definition of parameters;
Fu
b). Fser
tan-1(K)
(b)
Model for the serviceability limit state;
Kser
uu
uy
u
u ser
(c) and (d)
Model for the ultimate limit states
F
Rd
Rd
d).
c).
Ku
Ku
uu
R d /Ku
uu
Fig. 2–4 Connection models
Where
Ds – static ductility
uu – ultimate deformation (sliding or rotation)
uy – ultimate elastic deformation
user – deformation at the serviceability limit state, corresponding to Fser
Fser – force at the serviceability limit state
Rd – design value of the load-bearing capacity in the joint
(3)
Even if plastic deformation can occur in reality in the concrete and the
connecting elements at the strength limit state, the determination of the stresses can be
considered to be a linear-elastic behaviour of the composite element, in accordance with
Figure 2-5;
(4)
The effect of the plastic deformations intervenes by taking into consideration a
nominal secant modulus corresponding to the modulus of elasticity of the concrete and a real
secant modulus corresponding to the modulus of sliding of the connection;
(5)
The concrete stiffness, taken into consideration when calculating the unitary
stresses, shall be determined for the non-cracked cross-section. When checking the normal
unitary stresses corresponding to the sections of the composite structures, the tensile strength
of the concrete shall be disregarded;
(6)
On the compressed side, the limit compressive stress that the plastic
deformations of the concrete are related to shall be considered to be the compressive strength;
(7)
If the neutral axis is positioned in the concrete slab, a suitable reinforcement
shall be installed at the base of the concrete slab;
(8)
The modulus of sliding of the connection at the ultimate limit state is:
F
2–3
K u  0,6 est
 0, 6
– displacement relating to 60 % of the maximum shear force estimated
2
for simplification, the following can be considered: K u  K ser ;
3
0.6
14
Fig. 2–5
(9)
For cylindrical rod-type connectors (nails or screws), the following criteria
shall be admitted in order to determine the moduli of sliding Kser (and Ku, respectively), on the
basis of the theoretical curve for the displacement variation between the wood and concrete
“fˮ, as a function of the load “Pˮ in Fig. 2-6, as follows:
a. To determine the operating force, one shall start from the admissible displacement
value
dadm=0.09. This displacement corresponds to a shear force Pd1;
b.
For the limit shear force (load-bearing capacity at shearing) Pd2 a timber-concrete
displacement d=2.5dadm=0.225 shall be considered;
c.
The admissible shear force Padm shall be determined taking into consideration the
certainty coefficient 3.0 applied to the load-bearing capacity at shearing (Padm=Pd2/3);
d.
The modulus of sliding shall be determined using the ratio:
P
2–4
K ser  hot
d af
where: Phot 
2
Pd 2 [kN]
3
daf – the relative displacement [cm] between the timber and the concrete,
corresponding to load Phot
15
Fig. 2–6
(10) The exemplification and notations for this method of determining the moduli of
sliding are given in the informative annex, on the basis of shear tests carried out on timberconcrete composite specimens;
(11) Standard SR EN 1995-1-1 indicates the determination of the modulus of
sliding Kser, in a timber-timber joint that uses cylindrical rods, depending on the density of the
wood and the diameter of the connector, as follows:
Type of joint
Nails
Nails hit into pre-drilled holes, cotter pins, screws
Bolts
Note:
k
Kser [N/mm]
 k1,5 d 0,8
25
1, 5
k d
20
1, 5
k d
30
= characteristics value of the density of the wood
(12) Experimental tests carried out in the country and internationally using timberconcrete specimens have shown that the modulus of sliding of a timber-concrete connection
with cylindrical rods is more accurately expressed as a function of the diameter of the
connecting element “d” and the modulus of elasticity of the wood “Emean”, as follows:
K ser  0,08Emeand
2–5
16
2.2 Materials
2.2.1 Concrete
(1)
The characteristic (rated) and design strengths of the concrete, f ck and f cd , as
well as other design characteristics of concrete made using heavy or light ordinary aggregates,
shall be established in accordance with the provisions of SR EN 1992-1 and NE 012/2,
respectively;
(2)
The minimum recommended concrete class is C 20/25;
(3)
The maximum diameter recommended for the aggregates is dmax=16 mm, in
accordance with SR EN 12620;
(4)
To prevent the wood from getting wet during casting, but also to limit the
contraction phenomenon, the water-cement ratio should be as low as possible, in accordance
with the provisions of NE 012/1.
2.2.2 Wood
(1)
Solid wood
a. Solid wood beams can be made of coniferous solid wood, as well as deciduous
solid wood;
b.
The characteristic (rated) strengths of the wood, fmk, ftok and fvk, as well as other
design characteristics, shall be established in accordance with SR EN 1995-1-1.
(2)
Glued laminated timber
a. The characteristic (rated) strengths of glued laminated timber, fmk, ftok and fvk, as
well as
other design characteristics, shall be established in accordance with SR EN 1194.
(3)
Wooden beams in existing buildings
a.
The level of degradation of the existing wooden beams shall be assessed and
analysed in accordance with the provisions of P100-3;
b.
Any interventions on the wooden beams shall be carried out in accordance with
the provisions of P 100-3;
c.
Depending on the possibilities of accessing the structural elements, it is
recommended that test specimens are taken from the existing wooden beams in order to
determine the characteristic resistance to bending fmk, stretching parallel to the fibres ftok and
shearing fvk.
2.2.3 Reinforcements
(1)
The reinforcements installed in the concrete slabs of timber-concrete composite
floors shall be in the form of welded wire mesh or bars installed individually, forming wiretied nets;
f
f
(2)
The characteristic (rated) and design strengths yk and yd , as well as other
design characteristics shall be established in accordance with the provisions of SR EN 19921-1 and the provisions of the specific technical regulations in force with regard to the
performance requirements and criteria for steel products used as reinforcements.
2.2.4 Timber-concrete connectors
(1)
The connectors used shall be classified as follows:
a. Round nails with elongated shape or a dented surface, in accordance with STAS
2111 (Fig. 2-7);
17
b.
Semi-countersunk wood screws (STAS 1453), slotted countersunk screws
(STAS 1452), slotted button head screws (STAS 1451), hexagonal screws (STAS 1454),
square head screws (STAS 1455) (Fig. 2-7);
Fig. 2–7 Types of nails and screws
(2)
Connectors made of stainless steel or non-corrosive steel shall be used;
(3)
The values of the moduli of sliding Kser (and Ku, respectively) shall be
determined on the basis of the provisions stipulated in Point 2.1.3.
3
DESIGN OF TIMBER-CONCRETE COMPOSITE FLOORS
(1)
The calculation shall be carried out in accordance with the principles of the
limit state calculation method, taking into consideration:
- the different properties of the materials-strength;
- the different behaviour under load, over time, of the composite floor componentscreep, duration of application of the load;
(2)
The calculations for the timber-concrete composite floors must comply with
the ultimate limit state verification and the serviceability limit state verification, both for
short-term and long-term loads;
(3)
The ultimate limit state verification shall be carried out by determining the
maximum stresses in the components (wood, concrete, and connectors).
(4)
The serviceability limit state verification shall be carried out by determining
the maximum camber;
(5)
The stresses in the components of the composite floor at the ultimate limit state
and the serviceability limit state shall be checked during the initial stage (taking into
consideration the mean moduli of elasticity of the wood and concrete), as well as during the
final stage (taking into consideration the creep phenomenon that reduces the moduli of
elasticity of the components);
(6)
The purpose for carrying out a verification of the timber-concrete composite
floors at horizontal loads is to ensure the necessary strength and stiffness so that the floor can
be considered a rigid diaphragm in the horizontal plane. The seismic elevation forces shall be
determined in accordance with the provisions stipulated in P 100-1;
(7)
To calculate the sectional stresses (shear force and bending moment) caused by
the horizontal seismic forces in buildings with simple planar shapes that can be inscribed in a
rectangle, the timber-concrete composite floor shall be considered to be a continuous beam
18
supported on the structural walls. In this situation, the sectional stresses shall be calculated in
accordance with the calculation model given in CR 6;
(8)
Verification of the timber-concrete composite floor during the execution stages
is not necessary, due to the fact that temporary supports are provided during execution;
(9)
After the concrete has hardened, the wooden beam and the concrete slab are
connected and all the loads shall be absorbed by the composite element;
(10) A continuous timber-concrete composite floor can be calculated as a
succession of simply supported composite slabs, since the cross-section of the wooden beams
in the field areas usually provide a higher load-bearing capacity at bending than the bending
test proved necessary. The verification process for a composite floor in the areas of negative
bending moment is explained in Point 3.4.7.
3.1 Loads and stresses
(1)
The actions/loads for the design of timber-concrete composite floors shall be
classified and their structural effects shall be grouped in accordance with SR EN 1991-1-1;
(2)
The partial certainty coefficients for permanent and variable actions shall be
taken in accordance with SR EN 1990.
3.2 Calculation of the connection width of the slab
(1)
The connection width of the slab “bef” depends mainly on the ratio between the
width of the slab (the distance between beams “b”) and the span of the beam “l” and varies
along the beam span depending on the type of load and the static diagram. The connection
width of the slab shall be determined based on the transversal distribution of the tangential
stresses within the concrete footer (Fig. 3-1);
Fig. 3–1 Variation of tangential unitary stresses within the concrete footer
(2)
Various calculation standards propose covering relationships for determining
the connection width of the slab, valid for a continuous connection between the wooden
beams and the concrete slab;
(3)
Relationships 3–1 and 3–2 take into account the type of load in order to
determine the connection width of the concrete slab:
- for evenly distributed loads:
2

b 
bef  1  1,4  b
 l  

3–1
- for concentrated loads:
19
2

b
 b 
bef  1  1,4   0,8 b
l
 l 

3–2
(4)
The thickness of the slab shall be established from the requirement that the
stiffness ratio for the two connected elements is sub-unitary:
E1 I1
1
E2 I 2
3–3
3.3 General hypotheses
The calculation method for timber-wood composite floors shall take into consideration
the following hypotheses:
a. the wooden beam is simply supported;
b. the components of the composite floor are interconnected via connectors whose
reference feature is the modulus of sliding K;
c. the distance between connectors is constant or varies evenly as a function of the
shear force, between smin and smax, where smax ≤ 4smin; smin for the marginal area;
smax for the middle area (see Fig. 4-1).
3.4 Calculation at the ultimate limit state and the serviceability limit state
3.4.1 Characteristics of the composite section
(1)
The way in which the composite section works and the characteristics taken
into consideration are shown in Fig. 3-2;
(2)
The equivalent bending stiffness of the composite section shall be determined
using relationship 3–4:
( EI )ef  ( E1  I1   1  E1  A1  a12 )  ( E2  I 2   2  E2  A2  a22 )
3–4
where: E1, E2 - the values of the longitudinal modulus of elasticity for concrete and wood
A1, A2 - area of the concrete section (with bef calculated according to relationships 3–1
and 3–2) and the area of the wood section, respectively
I1, I2 - moment of inertia of the concrete section (with bef according to relationships
3–1 and 3–2) and the moment of inertia of the wood section, respectively
20
Connection
distance between
elements: s
modulus of sliding: K
stress: F
Note:
1 - concrete slab
2 - wooden beam
3 - connector
(3)
follows:
Fig. 3–2 Composite section
The stiffness reduction factor  shall be determined using relationship 3–5, as
- for the concrete slab:  1 
1
  E1  A1  sef
2
1
3–5
K l2
- for the wooden beam: 2=1
where: sef
K
- the equivalent distance between connectors
- modulus of sliding for the connector which, for calculation at the ultimate
limit state, is Ku, whilst for the limit state during normal operation is Kser
l
- length of the simply supported beam
(4)
The distances from the centre of gravity of the concrete section and of the
wooden section to the centre of gravity of the composite section, a1 and a2 respectively, shall
be determined using relationships 3–6 and 3–7, as follows:
a1 
h1  h2
 a2
2
3–6
a2 
 1  E1  A1  (h1  h2 )
 1  E1  A1   2  E2  A2
3–7
where: h1
h2
(5)
- thickness of the concrete slab
- height of the wooden beam
The thickness of the slab shall be verified using relationship 3–3.
21
3.4.2 Distance between connectors
(1)
The distance between connectors varies as a function of the sliding stress
between a minimum value smin at the level of the supports and smax in the middle area of the
beam. For simplification, the calculations shall consider an equivalent distance, as follows:
sef = 0.75 smin + 0.25 smax
(2)
3–8
Point 3.3(1) shall be complied with.
3.4.3 Verification of efforts in the composite section at the ultimate limit state in
the initial stage
(1)
The normal compressive and tensile stresses in the concrete slab and the
extremely stretched wood fibre shall be determined using the following relationships:
 c1d 
 m1d 
 t 2d 
 m2d 
 1  E1  a1  M Ed
3–9
( EI ) ef
0,5  E1  h1  M Ed
( EI )ef
3–10
 2  E2  a2  M Ed
3–11
( EI )ef
0,5  E2  h2  M Ed
( EI )ef
3–12
where: MEd
- design bending moment
(2)
- at the top:
The stresses in the concrete slab shall meet the following conditions:
 cd   c1d   m1d  f cd
3–13
- at the base:
 td   m1d   c1d  f ctd
3–14
(3)
The stresses on the lower side of the wood section shall be verified using the
condition:
 t 2d  m2d

1
3–15
f tod
f md
where: f cd , f ctd
- design compressive strength and axial tensile strength of the concrete,
in accordance with SR EN 1992-1-1.
f t 0 d , f md
- design tensile and bending strength of the wood, in accordance with
SR EN 1995-1-1.
22
(4)
The tangential stresses in the centre of gravity of the composite section shall be
checked as follows:
 max 
0,5 E 2  b2  h 2  VEd
 f vd
b2  ( EI ) ef
3–16
h2
 a2 - the distance from the stretched side of the wood section and the centre
2
of gravity of the composite section
VEd
- design shear force
where: h 
(5)
condition:
Fid 
The design value of the force in the joint shall comply with the following
 1  E1  A1  a1  smin VEd
( EI ) ef
where: Rd
Point (8)
3–17
- design value of the load-bearing capacity in the joint in accordance with
(6)
M yd 
where: M yk
to 3–22
 Rd
The design plastic moment of the joint shall be determined as follows:
M yk
M
3–18
- the characteristic plastic moment of the joint, according to relationships 3–19
M
- coefficient partially applied to the properties of the material
(7)
The characteristic plastic moment of a metal rod joint, determined using the
empirical formulas given in SR EN 409, has the values:
- for joints with round nails with a smooth surface: M yk  180d 2,6
3–19
- for square nails: M yk  270d 2,6
3–20
- for bolts and cotter pins: M yk 
- for screws: M yk 
0,8 fuk d 3
6
3–21
0,583 f uk d 3
6
3–22
where: fuk
- the characteristic value of the tensile strength of the joining element, in
accordance with Tables 3-1 and 3-2
d
- diameter of the rod in the smooth area of screws or the square side of square
nails (mm)
Table 3-1 Ultimate characteristic tensile strength for ordinary bolts
Bolt class
fuk N/mm2
4.6
400
4.8
320
23
5.6
500
5.8
500
6.8
600
Table 3-2 Ultimate characteristic tensile strength for ordinary steel bars
Type of steel
fuk N/mm2
S235
400
S275
400
S355
500
(8)
The strength of the joint shall be determined as a minimum value from the
following conditions:
- concrete yielding upon local compression on the contact surface between the
concrete and the connector:
f E
3–23
Rd  0,23d 2 ck cm
c
c
partial coefficient for concrete
fck - characteristic value of the compressive strength of concrete, measured on
cylinders after 28 days
- shear rupture of the connector:
0,8 f uk d 2
Rd 
4 M
3–24
- wood yielding:
Rd  1,5 2 M yd f h 2 d d
3–25
fh2d - design value of the local crushing strength of the wooden element
3.4.4 Verification of efforts in the composite section at the ultimate limit state in
the final stage
(1)
The creep phenomenon of timber-concrete composite elements is influenced by
the behavioural characteristics of the components over time, as well as the existing
environmental conditions (temperature, humidity);
(2)
The different behaviour of the components of a timber-concrete floor under
long-term loads shall be taken into consideration by reducing the moduli of elasticity of the
wood and concrete and the modulus of sliding of the connector, as follows:
- for concrete: Ecm , fin  Ecm (
1
)
1   ( , t 0 )
3–26
 (, t 0 ) - creep coefficient for concrete, in accordance with SR EN 1992-1-1
%G
%Q
- for wood: Emean, fin  Emean (

)
1  1  kdef 1  kdef
3–27
kdef - coefficient which takes into consideration the deformation as a function of the
time under the effect of creep and humidity, in accordance with SR EN 1995-1-1, for wood
and wooden materials
%G, %Q - percentage of the permanent and variable load, respectively
24
- for connectors: K u , fin 
Ku
1  k def
3–28
Ku,fin - final value of the instantaneous modulus of sliding for the ultimate limit state
kdef - joint coefficient, in accordance with SR EN 1995-1-1
(3)
The calculation shall be carried out with the relationships given in 3.4.1 and
3.4.3, using the moduli of elasticity of the wood and concrete, as well as the modulus of
sliding, calculated in accordance with Point 3.4.4.
3.4.5 Verification at the serviceability limit state in the initial stage
(1)
Verification of the camber in the initial stage shall be carried out taking into
consideration the mean moduli of elasticity for concrete Ecm and wood Emean, and the modulus
of sliding Kser, respectively;
(2)
The calculation and verifications for the composite element shall be repeated,
in accordance with Points 3.4.1 and 3.4.3;
(3)
The final instantaneous camber shall be calculated in accordance with SR EN
1995-1-1, as follows:
winst  winst,G  winst,Q
3–29
winst,G; winst,Q - instantaneous camber for the permanent action G and the variable
action Q, respectively
(4)
The final instantaneous camber must be within the recommended limit value
range specified in SR EN 1995-1-1.
3.4.6 Verification at the serviceability limit state in the final stage
(1)
Verification of the cambers in the final stage shall be performed by taking into
consideration the moduli of elasticity transformed depending on the deformations over time
and the load for concrete and wood, and by reducing the modulus of sliding Kser, as follows:
- for permanent actions:
1
)
- concrete: Ecm , fin  Ecm (
1   ( , t 0 )
 (, t 0 ) - creep coefficient for concrete, in accordance with SR EN 1992-1-1
1
- wood: Emean, fin  Emean (
)
1  1  kdef
K ser
- connectors: K ser , fin 
1  kdef
- for variable actions:
1
)
- concrete: Ecm , fin  Ecm (
1   ( , t 0 )
1
- wood: Emean, fin  Emean (
)
1  kdef
K ser
- connectors: K ser , fin 
1  kdef
3–30
3–31
3–32
3–33
3–34
3–35
25
(2)
The calculation and verifications for the composite element shall be repeated,
in accordance with Points 3.4.1 and 3.4.3;
(3)
The final camber shall be calculated in accordance with SR EN 1995-1-1, as
follows:
w fin  w fin,G  w fin,Q
3–36
wfin,G, wfin,Q - final camber for a permanent action G and a variable action Q, respectively
(4)
The final camber must be within the recommended limit value range specified
in SR EN 1995-1-1.
3.4.7 Verification of the composite floor in the areas of negative bending
moment
(1)
The capable bending moment of the composite section in the longitudinal
direction of the wooden beams shall be determined similarly to the one for a reinforced
concrete section, on the basis of the distribution of the normal unitary stresses, in accordance
with Fig. 3-3. The contribution of the wood cross-section shall be disregarded.
Fig. 3–3 Distribution of the normal unitary stresses for a negative moment
Where:
Ns
MRd
Ncm
z
As
as
fibre
xpl
concrete
ds
- resultant of the tensile stresses
- negative bending moment
- resultant of the normal unitary compressive stresses
- lever arm
- section of the strengthening reinforcement placed on the support, in mm2/m;
- distance from the centre of gravity of the reinforcement to the upper concrete
of the composite slab
- distance between the plastic neutral axis and the most compressed fibre of the
section
- net height of the concrete section
M Rd  N s z
3–37
(2)
The resultant of the tensile stresses N s inside the reinforcement placed on the
support and the lever arm z shall be determined with the following relationships:
N s  As f sd
3–38
26
z  h - 0,5xpl - a s
3–39
(3)
The resultant of the normal unitary tensile stresses inside the concrete,
calculated for a unitary slab width b = 1 m, is:
N cm  b x pl f cd
3–40
The position of the neutral axis x pl shall be determined from the projection equation
N s  N cm :
x pl  N s / bf cd
4
3–41
CONSTRUCTIVE PROVISIONS
4.1 Dimensions
(1)
If the concrete slab acts as a horizontal diaphragm, the minimum thickness
shall be h1=80 mm in accordance with the provisions of the normative documents in force
(with regard to strength, stiffness, sound insulation, etc.);
(2)
The minimum thickness of the concrete slab can be h1 = 60 mm in other
situations than those stipulated in (1);
(3)
The recommended maximum span of the wooden beams is:
o
- for solid wood beams:
lmax = 5.0 metres
o
- for glued wood beams:
lmax = 8.0 metres
(4)
The recommended ratio between the height of the wooden beams h2 and the
l
 25...16 .
span of the floor l is:
h2
4.2 Reinforcement
(1)
The reinforcement used must comply with the provisions stipulated in Point
2.2.3;
(2)
The minimum concrete coating is cmin = 10 mm;
(3)
The admissible tolerances for positioning the reinforcements shall meet the
requirements enforced by the provisions of SR EN 1992-1-1 and NE 012-2;
(4)
If the calculations reveal that reinforcement is not necessary, a constructive
reinforcement shall be installed at the base of the concrete slab, as follows:
a. the distance between bars, both in the horizontal and the longitudinal direction,
must not exceed 250 mm;
b. the minimum area of the reinforcement in each direction is 250 mm2/m;
c. the minimum diameter of the reinforcements is dmin = 6 mm;
(5)
For various reasons, reinforcements made of wire-tied mesh, which are used to
reinforce composite slabs, shall be located in certain areas, as follows:
a. in the support areas, at the top of the slab: having a strengthening role in absorbing
the negative moments;
b. in the field areas, at the base of the slab: having a strengthening role in absorbing
the positive moments;
27
(6)
If the floor was calculated as a succession of simply supported slabs, a
minimum reinforcement shall be installed at the top of the support, in accordance with both
conditions below:
a. percentage of the concrete section: As,min = 0.4 %Ac;
b. minimum 80 mm2/m.
(7)
The reinforcement used must comply with the provisions stipulated in Point
2.2.3;
(8)
The length on which the reinforcements are anchored in the reinforced concrete
girders must comply with the provisions stipulated in CR 6.
4.3 Connectors
(1)
Nail connectors shall be distributed in one or two alternating, crossed rows,
perpendicular to the wooden beam. The minimum diameter of the nails is dmin = 8 mm;
(2)
Screw connectors shall be distributed in one or two alternating, crossed rows,
inclined at a 45 angle from the wooden beam. The minimum diameter of the screw is dmin = 6
mm;
(3)
The connectors shall be positioned on the wooden beam in accordance with
Fig. 4-1.
Fig. 4–1 Distribution of connectors
(4)
The distance between connectors should be within the following values:
smin = 80 mm–150 mm
smax = 150 mm–300 mm
4.4 Support
(1)
Timber-concrete composite floors are supported along their entire contour on
load-bearing brick masonry walls, via reinforced concrete girders. Concentrated supports
(pillars) are excluded;
(2)
For new buildings, the following shall be complied with:
a. the support requirements for wooden beams stipulated in SR EN 1995-1-1;
b. the requirements for anchoring the concrete slab along its entire contour using
reinforced concrete girders made in accordance with the provisions of CR 6;
(3)
A new method of supporting the composite floor in new buildings is shown in
Fig. 4-2;
(4)
For existing buildings, procedures shall be chosen depending on the results of
an assessment and analysis carried out in accordance with P100-3. The concrete slab shall be
anchored in girders created on the inside surface of the walls (Fig. 4-3), on the outside surface
(Fig. 4-4), or under the wooden beams (Fig. 4-5); the continuity of the concrete slab near the
intermediary supports shall be ensured by casting the concrete from the slab into openings
created in the existing masonry. The dimensions of the reinforcement installed in these
openings shall be chosen in such a way as to ensure that stresses are transmitted from one
opening of the slab to another;
28
(5)
When wooden elements come in contact with other materials and moisture
occurs for various reasons, the wood shall be protected by water-insulating layers or, if
possible, the contact is made by parts made of moisture-resistant materials, so that free spaces
are created for the continuous aeration of the wooden elements;
(6)
The wooden beam sections that are in contact with the masonry shall be
protected in the area of the support by means of water-proof insulation consisting of one or
two layers of cardboard or bituminous fabric. The beam end shall be installed at a distance of
approximately 2 cm from the masonry, creating a ventilation space.
Section A-A
2
Section 1-1
Section 2-2
connectors
Section A-A
Section 1-1
connectors
A
Fig. 4–2 Support version for new buildings
29
Section 2-2
Section 1-1
connectors
Fig. 4–3 Existing buildings: anchoring using girdles created on the inner surface of the walls
Section A-A
2
Fig. 4–4 Existing buildings: anchoring using girdles created on the exterior surface of the
walls
30
Section A-A
Section 1-1
Section 2-2
connectors
Fig. 4–5 Existing buildings: anchoring using girdles created under the wooden beams
4.5 Operability (serviceability)
(1)
To ensure the durability of timber-concrete composite floors, the following are
required during the operating process:
a. the wooden elements of the floor are not exposed to humidity action;
b.
protective measures are taken to avoid the occurrence of condensation or too
high humidity in the rooms;
c.
any separation walls or stoves must be built on the floors only after a technical
survey and on the basis of a design, in accordance with the regulations in force;
d.
airing and ventilation measures are taken for enclosed spaces (basements, attics);
e.
all sanitary, electrical, or gas utility routes shall be positioned in accordance with
the regulations in force;
(2)
The systems for protecting the wooden elements against chemical and
biological agents shall be chosen depending on the type and condition of the wooden beams,
the type and level of aggression of the environment, as well as the estimated durability of the
protection;
(3)
The type and level of aggression of the environment shall be established by the
design engineer following assessment of the results of qualitative and quantitative analyses of
the aggressive (chemical and biological) agents, relative humidity, and air temperature. The
chemical and biological aggressive agents which act upon wooden constructions or wood
components are classified in accordance with the provisions of ST 049;
(4)
The definition of the operating classes from an environmental aggression point
of view shall be established in accordance with the provisions of ST 049, SR EN 335-1, and
31
SR EN 1995-1-1, as well as the provisions stipulated in the specific technical regulations for
the design of wooden constructions, in force;
(5)
The classes of biological hazard shall be established in accordance with SR EN
335-1 and the specific technical regulations for the design of wooden constructions, in force;
(6)
The protection systems applied on the surface of wooden elements against
aggressive agents must comply with the performance criteria, as well as the essential,
functional, and technological requirements stipulated in ST 049;
(7)
The performance levels and criteria for wooden beams and their protection
systems are defined in ST 049 for:
a. the support layer: wooden beams or lost shuttering;
b.
the systems for protection against physico-chemical agents, presented as real,
minimum values, in order to obtain efficient protection of the wood;
c.
the systems for protection against biological agents;
(8)
For the entire building to have a certain degree of fire resistance, its main
components must meet the minimum combustibility and fire resistance requirements, in
accordance with the legislation in force;
(9)
Applying a fireproofing treatment to the wooden beams that are an integrated
part of the composite floor shall ensure that the minimum necessary requirements are
complied with, in accordance with the legislation in force relating to the classification and
grouping of construction products based on their fire behaviour performance;
(10) Fireproofing products must comply with the general provisions, the surface
preparation requirements, as well as the application requirements and technology stipulated in
the specific technical regulations in force.
32
5
BEHAVIOUR OVER TIME
(1)
The behaviour over time shall be tracked in accordance with the legislation in
force regarding the behaviour of buildings over time. Everyday tracking is understood to be
the activity of tracking the behaviour of the building by observing and recording certain
aspects, phenomena, and parameters that could indicate modifications in the buildingʾs
ability to meet the strength, stability, and durability requirements established by design;
(2)
Everyday tracking has a permanent nature, its duration coinciding with the
effective serviceability period of the building;
(3)
Specific provisions for the everyday tracking of new buildings with timberconcrete composite floors:
One shall aim to identify the following phenomena, either by visual inspection or by
using measuring devices: settling in the supporting area of the wooden beams, longitudinal
cracks in the wooden beams, excessive vertical deformations in the middle of the floor span,
the occurrence of local wet patches on the existing finishing, or the presence of mould;
The main areas targeted by everyday tracking are: the support areas and the areas in
the middle of the span of the wooden beams;
Depending on the finishing applied at the base of the composite floor, access to the
elements that require inspection shall be provided;
(4)
Specific provisions for the everyday tracking of existing buildings with
timber-concrete composite floors:
One shall aim to identify the following phenomena, either by visual inspection or by
using measuring devices: settling in the supporting area of the wooden beams, longitudinal
cracks in the wooden beams, excessive vertical deformations in the middle of the floor span,
the occurrence of local wet patches on the existing finishing or the presence of mould, the
occurrence of degradation in the girdles that have been newly cast on the existing masonry;
The main areas targeted by everyday tracking are: the support areas and the areas in
the middle of the span of the wooden beams, as well as other areas that shall be established
together with the technical expert.
Depending on the finishing applied at the base of the composite floor, access to the
elements that require inspection shall be provided.
(5)
Any changes to the intended use of the facility shall be carried out following
a technical survey and in accordance with the regulations in force.
6
EXECUTION PROVISIONS AND TECHNOLOGY
6.1 Provisions for new buildings
The general procedure for creating a timber-concrete composite floor in new buildings
is as follows:
(1)
(2)
(3)
(4)
Distributing the wooden beams on the load-bearing masonry walls, at the
distances specified in the design;
waterproofing of the ends of the wooden beams before laying down the wooden
beams;
Providing temporary supports for the wooden beams, usually at 1/3 of their
span;
Making the form by placing it at the top of the wooden beams or in the gaps
between the wooden beams;
33
(5)
(6)
Laying down a PVC sheet or asphalt felt to protect the wooden beams against
wetting as a result of concrete casting;
Distributing the connectors at the distances stipulated in the design;
(7)
Positioning the reinforcements in the concrete slab and fixing them in the
reinforced concrete girdles located on the contour, in accordance with the design;
(8) Checking that the connectors and the reinforcements have been positioned in
accordance with the design;
(9) Casting the concrete for the slab and girdles in accordance with the regulations
in force;
(10) Protecting the freshly cast concrete against dehydration.
6.2 Provisions for existing buildings
The general procedure for creating a timber-concrete composite floor in existing
buildings is as follows:
(1) Assessing the level of degradation of the existing wooden beams. One shall look
for degradation such as:
a. rotting of the wooden beam ends
b. the occurrence of defects or cracks in the beam field
c. the occurrence of large deformations due to load modifications
(2) Remedying the degradations/consolidation of the wooden beams. The most
common solutions are:
a. to replace the wooden beams whose ends are rotten
b. to install antiseptic lateral straps made of wooden floor boards, which shall be
connected to the existing beam by nails or screws
c. to install U-shaped supports, connected to the existing beam by bolts
(3) Inserting new wooden beams between the existing beams;
(4) Providing temporary supports for the wooden beams, usually at 1/3 of their
span;
(5) Removing the existing flooring, the insulation layers (soil, slag, etc.), and the
ceiling, if this is damaged;
(6) Creating a form for the perimetral girdles provided in order to anchor the
reinforcements of the composite floor;
(7) Making the form for the composite floor by placing it at the top of the wooden
beams or in the gaps between the wooden beams;
(8) Laying down a PVC sheet or asphalt felt to protect the wooden beams against
wetting as a result of concreting;
(9) Distributing the connectors at the distances stipulated in the design;
(10) Placing the reinforcements in the concrete slab and fixing it into the reinforced
concrete girdles located along the contour; for continuous slabs, openings shall
be created to ensure continuity with the neighbouring slab;
(11) Checking that the connectors and the reinforcements have been positioned in
accordance with the design;
(12) Casting the concrete for the girdles and the slab in accordance with the
regulations in force;
(13) Protecting the freshly cast concrete against dehydration.
34
ANNEX A
SHEAR TESTING USING TEST SPECIMENS
General aspects
(1)
The specific tests are used in order to determine the modulus of sliding for the
connectors, other than those referred to in the present guidelines;
(2)
The shear test shall be carried out in accordance with the provisions stipulated
in SR EN 26891;
Shear testing using test specimens
(1)
(2)
At least six test specimens shall be prepared, in accordance with Fig. A-1,
The connectors shall be located at a distance “s” from each other.
1 - wooden beams
2 - concrete bulb
3 - connectors
Fig. A–1 Methods for creating the test specimens
(3)
The parameters used for the loading procedure shall be defined on the basis of
an initial estimation of the maximum load Fest. This value shall be obtained from experience,
by calculation, or from the results of preliminary tests carried out on a timber-concrete test
specimen, shall be maintained for the entire duration of the tests, and shall only be modified
if, during the tests, the mean value of the maximum force varies by more than 20 % from the
estimated value Fest;
Carrying out experimental tests
(1)
Any specimens shall be tested on a specialised stand;
(2)
The test shall be carried out by monitoring the load up to 70 % of the
maximum estimated shear force; after this point, the deformation shall be checked;
(3)
The test shall be considered to be completed when:
a. the maximum estimated shear force Fest is reached
b. the displacement between the wood and the concrete is 15 mm.
(4)
The total duration of a specimen test must be between minimum 10 minutes
and maximum 15 minutes. The load-time curve is drawn in Figure A-2;
35
Force
time (s)
Fig. A–2 Load-time curve
Determination of the load-bearing capacity and modulus of sliding
(1)
The maximum force Fmax is obtained from the force-displacement diagram
drawn using the values obtained from experimental tests;
(2)
The modulus of sliding of the joint Kser shall be determined as a function of the
maximum estimated shear force and the deformation corresponding to the value of two forces
during the test, as follows:
K ser 
0,4  Fest
A–1
4
(ν0,4 ν 0,1 )
3
where:  0, 4 -
 0 ,1 Fest-
the deformation corresponding to 40 % of Fest;
the deformation corresponding to 10 % of Fest;
the force estimated by calculation or initial tests
36
ANNEX B CALCULATION EXAMPLES
Example 1: Timber-concrete composite floor with several openings
This presents the design of an intermediary floor in a new residential building made up
of ground floor + 1 storey, with the planar dimensions 9.05 x 9.05 metres and the elevation
height het = 2.90 m.
The structure is made up of confined masonry (ZC) with the exterior wall thickness of
38 cm and interior wall thickness of 30 cm. The seismic area is ag =0.16 g.
The floor shall be built in a timber-concrete composite solution, using solid wood
beams.
Horizontal section
1
2
3
905
37,5
500
37,5
30
25
427,5
12,5 25
830
905
830
15 15
300
B
37,5
427,5
30
25
37,5
25 12,5
37,5
25
C
37,5
400
400
427,5
37,5
300
15 15
500
A
37,5
25
37,5
500
12,5
30
905
30
B
300
327,5
400
400
427,5
25
12,5 25
37,5
25
37,5
C
30
527,5
25
1
2
3
The wooden beams shall be placed in the short direction of the slab eyelets in
accordance with the horizontal section below. The distance between beams (interax) shall be
chosen as follows:
𝑏 = 50 𝑐𝑚
37
A
Positioning of the wooden beams
concret
e
screw
wooden
beam
Timber-concrete composite section
Design of the composite floor
1. Characteristics of the chosen component materials
38
1.1. Wood – beams: coniferous solid wood Class C27; serviceability Class 1.
Characteristic values – in accordance with SR EN 1995–1–1
- bending:
𝑓𝑚𝑘 = 27 𝑁⁄𝑚𝑚2
𝑓𝑡0𝑘 = 16 𝑁⁄𝑚𝑚2
-
stretching along the fibre:
-
shearing:
𝑓𝑣𝑘 = 2,8 𝑁⁄𝑚𝑚2
-
modulus of elasticity:
𝐸𝑚𝑒𝑎𝑛 (𝐸2 ) = 12000 𝑁⁄𝑚𝑚2
-
density:
𝜌0𝑘 = 380
𝑘𝑔⁄
𝑚3
Partial certainty coefficients:
- coefficient that takes into account the effect of the load duration and humidity, in
accordance with
SR EN 1995-1-1 Table 3.1., Note (2)
𝑘𝑚𝑜𝑑 = 0,60
- coefficient for the material and strength, in accordance with SR EN 1995-1-1,
Table 2.3.
𝛾𝑀 = 1,30
- coefficient which takes into account the deformations over time and the load
duration
𝑘𝑑𝑒𝑓,𝑝𝑒𝑟𝑚 = 0,60
𝑘𝑑𝑒𝑓,𝑚𝑒𝑑𝑖𝑒 = 0,60
Design values:
- bending:
𝑓𝑚𝑑 =
-
stretching along the fibre:
-
shearing:
k mod × fmk
γM
𝑓𝑡0𝑑 =
𝑓𝑣𝑑 =
=
1,3
= 12,46 𝑁⁄𝑚𝑚2
𝑘𝑚𝑜𝑑 × 𝑓𝑡0𝑘
𝑘𝑚𝑜𝑑 × 𝑓𝑣𝑘
𝛾𝑀
0,60×27
𝛾𝑀
=
=
0,60 × 2,8
1,3
1.2.Concrete – slab: Class C 25/30
Characteristic values: in accordance with SR EN 1992-1-1
- per cube:
𝑓𝑐𝑘𝑐𝑢𝑏𝑒 = 30 𝑁⁄𝑚𝑚2
- per cylinder:
𝑓𝑐𝑘 = 25 𝑁⁄𝑚𝑚2
- mean value at axial tension: 𝑓𝑐𝑡 = 2,6 𝑁⁄𝑚𝑚2
- modulus of elasticity:
𝐸𝑐𝑚 (𝐸1 ) = 31000 𝑁⁄𝑚𝑚2
Partial certainty coefficients
39
0,60 × 16
1,3
= 7,38 𝑁⁄𝑚𝑚2
= 1,29 𝑁⁄𝑚𝑚2
-
coefficient for the ultimate limit state, in accordance with SR EN 1992-1-1, Table
2.1.
1,5  permanenta, tranzitorie
Yc  
1,25  accidentala
-
coefficients that take into account the long-term effect and unfavourable effects
resulting from the way in which the loads are applied
acc : 0,8...1 din SR EN 1992  1  1; acc  0,85
act : recomandat 1; act  0,85
𝑘𝑡 = 0,85
Design values
- per cube:
𝑓𝑐𝑑 =
-
𝑓𝑐𝑡𝑑 =
axial tension:
𝛼𝑐𝑐 × 𝑓𝑐𝑘𝑐𝑢𝑏𝑒 × 𝑘𝑡
𝛾𝑐
𝛼𝑐𝑡 × 𝑓𝑐𝑡
𝛾𝑐
=
=
0,85×2,6
1,5
0,85×0,85×30
1,5
= 14,45 𝑁⁄𝑚𝑚2
= 1,47 𝑁⁄𝑚𝑚2
1.3.Connectors
Type of connector: Hexagonal screw with the length L = 10 cm
Diameter of connector: d=12 mm
Characteristic values:
- tension: 𝑓𝑢𝑘 = 500 𝑁⁄𝑚𝑚2
-
modulus of sliding (relationship 2–5):
-−
for the
𝐾𝑠𝑒𝑟 = 0,08 × 𝑑 × 𝐸𝑚𝑒𝑎𝑛 = 0,08 × 12 × 12000 = 11520 𝑁⁄
𝑚𝑚 serviceability
𝑝𝑒𝑛𝑡𝑟𝑢 𝑆𝐿𝑆
limit state
2
2
𝐾𝑢 = 3 𝐾𝑠𝑒𝑟 = 3 × 11520 = 7680 𝑁⁄
− 𝑝𝑒𝑛𝑡𝑟𝑢 𝑆𝐿𝑈
𝑚𝑚 - for the
Partial certainty coefficients
ultimate limit
- coefficient for connection (joining),state
in accordance with SR EN 1995-1-1, Table
2.3.
𝛾𝑀 = 1,3
-
coefficient which takes into account the deformations over time and the load
duration
𝑘𝑑𝑒𝑓,𝑝𝑒𝑟𝑚 = 0,60
𝑘𝑑𝑒𝑓,𝑚𝑒𝑑𝑖𝑒 = 0,60
2. Geometric characteristics of the chosen components
2.1.Wooden beam
- width:
- height:
𝑏2 = 190 𝑚𝑚
ℎ2 = 250 𝑚𝑚
-
𝐼2 =
moment of inertia:
40
𝑏2 ×ℎ23
12
=
190×2503
12
= 2,47 × 108 𝑚𝑚4
area:
𝐴2 = 𝑏2 × ℎ2 = 190 × 250 = 47500 𝑚𝑚2
span:
𝑙 = 4000 𝑚𝑚
distance between the beams (interax): 𝑏 = 500 𝑚𝑚
-
2.2.Concrete slab
-
thickness:
ℎ1 = 80 𝑚𝑚
- connection width calculated for evenly distributed loads in accordance with
relationship 3–3:
2
2
𝑏𝑒𝑓 = [1 − 1,4 × (𝑏⁄𝑙 ) ] × 𝑏 = [1 − 1,4 × (500⁄4000) ] × 500 = 489 𝑚𝑚
𝑏𝑒𝑓 ×ℎ13
= 2,09 × 107 𝑚𝑚4
moment of inertia:
𝐼1 =
-
area:
𝐴1 = 𝑏𝑒𝑓 × ℎ1 = 489 × 80 = 39125 𝑚𝑚2
12
=
489×803
-
12
2.3.Verification of the slab thickness (relationship 3–3):
𝐸1 × 𝐼1 31000 × 2,09 × 107
=
= 0,22 ≤ 1
𝐸2 × 𝐼2
12000 × 2,4 × 108
3. Loads and stresses
The calculation shall be carried out as for a simply supported beam with the span l = 4.00
m.
3.1. Characteristic values, partial certainty coefficients, and design values
Permanent
Type of load
Net weight of the
reinforced concrete
slab
Flooring
Light partition walls
Net weight of the
wooden beams
Net
Characteristics
Partial
certainty
coefficient
Calculation
2000 𝑁⁄
𝑚2
1.35
2700 𝑁⁄
𝑚2
1300 𝑁⁄
𝑚2
1000 𝑁⁄
𝑚2
1.35
1755 𝑁⁄
𝑚2
1350 𝑁⁄
𝑚2
180 𝑁⁄
𝑚
2000 𝑁⁄
𝑚2
1.35
1.35
243 𝑁⁄
𝑚
3000 𝑁⁄
𝑚2
1.50
3.2.Linear stresses
-
Permanent load:
𝑔𝑑 = (2700 + 1755 + 1350) × 0,50 + 243 = 3145 𝑁⁄𝑚
-
Net load
𝑞𝑑 = 3000 × 0,50 = 1500 𝑁⁄𝑚
3.3.Stresses
-
Bending moment: 𝑀𝐸𝑑 =
(𝑔𝑑 +𝑞𝑑 )×𝑙2
8
=
41
(3,145+1,5)×40002
8
= 9,3 × 106 𝑁𝑚𝑚
-
Shear force: 𝑉𝐸𝑑 =
(𝑔𝑑 +𝑞𝑑 )×𝑙
2
=
(3,145+1,5)×4000
2
= 9,3 × 103 𝑁
4. Joint verification
4.1.Plastic moment of the joint (relationship 3–22)
𝑀𝑦𝑘 0,583 × 𝑓𝑢𝑘 × 𝑑 3
0,583 × 500 × 123
𝑀𝑦𝑑 =
=
=
= 64,6 × 103 𝑁𝑚𝑚
𝛾𝑀
6 × 𝛾𝑀
6 × 1,3
4.2.Strength of the connection upon yielding of the concrete (relationship 3–23)
𝑅𝑑 = 0,23 × 𝑑2 × √
𝑓𝑐𝑘 × 𝐸𝑐𝑚
25 × 31000
= 0,23 × 122 × √
= 26078,71 𝑁
𝛾𝑐
1,25
4.3.Shear rupture strength of the connection (relationship 3–24)
𝑓𝑢𝑘 × 𝜋 × 𝑑 2
500 × 3,14 × 122
𝑅𝑑 = 0,8 ×
= 0,8 ×
= 34781,54 𝑁
4 × 𝛾𝑀
4 × 1,3
4.4.Strength upon yielding of the wood (relationship 3–25)
𝑅𝑑 = 1,5 × √2 × 𝑀𝑦𝑑 × 𝑓ℎ2𝑑 × 𝑑 = 1,5 × √2 × 64,6 × 103 × 12,66 × 12 = 6640 𝑁
where:
𝑓ℎ2𝑘 = 0,082 × (1 − 0,01 × 𝑑) × 𝜌𝑘 = 0,082 × (1 − 0,01 × 12) × 380
= 27,42 𝑁⁄𝑚𝑚2
One shall introduce ρk in kg 3 , and d in mm, respectively
m
𝑘𝑚𝑜𝑑 × 𝑓ℎ2𝑘 0,6 × 27,42
𝑓ℎ2𝑑 =
=
= 12,66 𝑁⁄𝑚𝑚2
𝛾𝑀
1,3
5. Verification of stresses at the ultimate limit state in the initial stage
5.1. Characteristics of the composite section (relationship 3–4)
(𝐸𝐼)𝑒𝑓 = (𝐸1 × 𝐼1 + 𝛾1 × 𝐸1 × 𝐴1 × 𝑎12 ) + (𝐸2 × 𝐼2 + 𝛾2 × 𝐸2 × 𝐴2 × 𝑎22 )
= (31000 × 2,09 × 107 + 0,080 × 31000 × 39125 × 140,892 ) + 12000
× 2,47 × 108 + 1 × 12000 × 47500 × 24,112 = 5,88 × 1012 𝑁𝑚𝑚2
𝛾1 =
1+
𝜋2
1
1
=
= 0,080
2
3,14 × 31000 × 39125 × 117,5
× 𝐸1 × 𝐴1 × 𝑠𝑒𝑓
1+
7680 × 40002
𝐾𝑢 × 𝑙 2
𝛾2 = 1
𝑠𝑒𝑓 = 0,75 × 𝑠𝑚𝑖𝑛 + 0,25 × 𝑠𝑚𝑎𝑥 = 0,75 × 90 + 0,25 × 200 = 117,5 𝑚𝑚
𝛾1 × 𝐸1 × 𝐴1 × (ℎ1 + ℎ2 )
𝑎2 =
2 × (𝛾1 × 𝐸1 × 𝐴1 + 𝛾2 × 𝐸2 × 𝐴2 )
0,080 × 31000 × 39125 × (80 + 250)
=
= 24,11 𝑚𝑚
2 × (0,080 × 31000 × 39125 + 1 × 12000 × 47500)
42
𝑎1 =
ℎ1 + ℎ2
80 + 250
− 𝑎2 =
− 24,11 = 140,89 𝑚𝑚
2
2
5.2.Stresses in the concrete slab (relationship 3–9 and relationship 3–10)
𝛾1 × 𝐸1 × 𝑎1 × 𝑀𝐸𝑑 0,080 × 31000 × 140,89 × 9,3 × 106
𝜎𝑐1𝑑 =
=
(𝐸𝐼)𝑒𝑓
5,88 × 1012
= 0,55 𝑁⁄𝑚𝑚2
0,5 × 𝐸1 × ℎ1 × 𝑀𝐸𝑑 0,5 × 31000 × 80 × 9,3 × 106
𝜎𝑚1𝑑 =
=
= 1,96 𝑁⁄𝑚𝑚2
(𝐸𝐼)𝑒𝑓
5,88 × 1012
5.3.Verification of stresses in the concrete slab
at the top: 𝜎𝑐𝑑 = 𝜎𝑐1𝑑 + 𝜎𝑚1𝑑 = 0,55 + 1,96 = 2,51 ≤ 𝑓𝑐𝑑 = 14,45 𝑁⁄𝑚𝑚2
at the base: 𝜎𝑡𝑑 = 𝜎𝑚1𝑑 − 𝜎𝑐1𝑑 = 1,96 − 0,55 = 1,40 ≤ 𝑓𝑐𝑡𝑑 = 1,47 𝑁⁄𝑚𝑚2
-
5.4.Verification of stresses in the wooden beam (relationship 3–11 and 3–12)
𝛾2 × 𝐸2 × 𝑎2 × 𝑀𝐸𝑑 1 × 12000 × 24,11 × 9,3 × 106
𝜎𝑡2𝑑 =
=
= 0,46 𝑁⁄𝑚𝑚2
(𝐸𝐼)𝑒𝑓
5,88 × 1012
𝜎𝑚2𝑑 =
0,5 × 𝐸2 × ℎ2 × 𝑀𝐸𝑑 0,5 × 12000 × 250 × 9,3 × 106
=
= 2,37 𝑁⁄𝑚𝑚2
(𝐸𝐼)𝑒𝑓
5,88 × 1012
5.5.Verification of stresses in the wooden beam (relationship 3–15)
-
at the base:
𝜎𝑡2𝑑
𝑓𝑡0𝑑
+
𝜎𝑚2𝑑
𝑓𝑚𝑑
=
0,46
7,38
2,37
+ 12,46 = 0,25 ≤ 1
5.6.Verification of tangential stresses
ℎ2
250
ℎ=
+ 𝑎2 =
+ 24,11 = 149,11 𝑚𝑚
2
2
0,5 × 𝐸2 × 𝑏2 × ℎ2 × 𝑉𝐸𝑑
𝜏𝑚𝑎𝑥 =
≤ 𝑓𝑣𝑑
𝑏2 × (𝐸𝐼)𝑒𝑓
𝜏𝑚𝑎𝑥 =
0,5 × 12000 × 190 × 149,112 × 9,3 × 103
= 0,2107 ≤ 1,29 𝑁⁄𝑚𝑚2
190 × 5,88 × 1012
5.7.Verification of stresses in the connectors
𝛾1 × 𝐸1 × 𝐴1 × 𝑎1 × 𝑠𝑚𝑖𝑛 × 𝑉𝐸𝑑
𝐹1,𝑑 =
≤ min(R d )
(𝐸𝐼)𝑒𝑓
𝐹1,𝑑 =
0,080 × 31000 × 39125 × 140,89 × 90 × 9,3 × 103
= 1953,04
5,88 × 1012
≤ 6643,31 N
6. Verification of the floor at the ultimate limit state in the final stage.
43
The deformations over time shall be taken into consideration for all materials, as follows:
- The transformed modulus of elasticity of the wooden beams (relationship 3–27):
%𝐺
%𝑄
0,68
0,32
𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 = 𝐸𝑚𝑒𝑎𝑛 × (
+
) = 12000 × (
+
)
1 + 𝛹 × 𝑘𝑑𝑒𝑓 1 + 𝑘𝑑𝑒𝑓
1 + 0,50 × 0,60 1 + 0,6
= 8144 𝑁⁄𝑚𝑚2
- Modulus of sliding of the connection (relationship 2–5):
- for the
𝐾𝑠𝑒𝑟 = 0,08 × 𝑑 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 = 0,08 × 12 × 8144
serviceability
= 7814 𝑁⁄
− 𝑝𝑒𝑛𝑡𝑟𝑢 𝑆𝐿𝑆
limit state
𝑚𝑚
2
2
𝑁
𝐾𝑢 = 3 𝐾𝑠𝑒𝑟 = 3 × 7814 = 5212 ⁄
− 𝑝𝑒𝑛𝑡𝑟𝑢
- for the𝑆𝐿𝑈
𝑚𝑚
ultimate
limit
- The transformed modulus of elasticity of the concrete
(relationship
3–26):
state
1
1
𝐸𝑐𝑚 𝑓𝑖𝑛 = 𝐸𝑐𝑚 × (
) = 31000 × (
) = 7294,1 𝑁⁄𝑚𝑚2
1 + 𝜑(∞, 𝑡0 )
1 + 3,25
6.1. Characteristics of the composite section
The formulas given in Point 5 shall be used, introducing the transformed moduli of
elasticity for wood 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 , concrete, 𝐸𝑐𝑚 𝑓𝑖𝑛 and the transformed modulus of sliding for
connectors.
(𝐸𝐼)𝑒𝑓 = (𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐼1 + 𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × 𝑎12 )
+ (𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐼2 + 𝛾2 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐴2 × 𝑎22 )
= (7294 × 2,09 × 107 + 0,201 × 7294,1 × 39125 × 143,652 )
+ (8144 × 2,47 × 108 + 1 × 8144 × 47500 × 21,352 )
= 3,53 × 1012 𝑁𝑚𝑚2
1
1
𝛾1 =
=
= 0,201
2
2
3,14 × 7294,1 × 39125 × 117,5
𝜋 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × 𝑠𝑒𝑓
1+
1+
5212 × 40002
𝐾𝑢 × 𝑙 2
𝛾2 = 1
𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × (ℎ1 + ℎ2 )
𝑎2 =
2 × (𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 + 𝛾2 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐴2 )
𝑎2 =
0,201 × 7294,1 × 39125 × (80 + 250)
= 21,35 𝑚𝑚
2 × (0,201 × 7294,1 × 39125 + 1 × 8144 × 47500)
𝑎1 =
ℎ1 + ℎ2
80 + 250
− 𝑎2 =
− 21,35 = 143,65 𝑚𝑚
2
2
6.2.Stresses in the concrete slab
44
𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝑎1 × 𝑀𝐸𝑑
0,201 × 7294,1 × 143,65 × 9,3 × 106
𝜎𝑐1𝑑 =
=
(𝐸𝐼)𝑒𝑓
3,53 × 1012
= 0,556 𝑁⁄𝑚𝑚2
0,5 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × ℎ1 × 𝑀𝐸𝑑 0,5 × 7294,1 × 80 × 9,3 × 106
𝜎𝑚1𝑑 =
=
= 0,768 𝑁⁄𝑚𝑚2
(𝐸𝐼)𝑒𝑓
3,53 × 1012
-
6.3.Verification of stresses in the concrete slab
at the top:
𝜎𝑐𝑑 = 𝜎𝑐1𝑑 + 𝜎𝑚1𝑑 = 0,556 + 0,768 = 1,324 ≤ 𝑓𝑐𝑑 = 14,45 𝑁⁄𝑚𝑚2
at the base:
𝜎𝑡𝑑 = 𝜎𝑚1𝑑 − 𝜎𝑐1𝑑 = 0,768 − 0,556 = 0,212 ≤ 𝑓𝑐𝑡𝑑 = 1,47 𝑁⁄𝑚𝑚2
6.4.Stresses in the wooden beam
𝜎𝑡2𝑑 =
𝛾2 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝑎2 × 𝑀𝐸𝑑 1 × 8144 × 21,35 × 9,3 × 106
=
= 0,458 𝑁⁄𝑚𝑚2
(𝐸𝐼)𝑒𝑓
3,53 × 1012
0,5 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × ℎ2 × 𝑀𝐸𝑑 0,5 × 8144 × 250 × 9,3 × 106
𝜎𝑚2𝑑 =
=
(𝐸𝐼)𝑒𝑓
3,53 × 1012
= 2,679 𝑁⁄𝑚𝑚2
6.5.Verification of stresses in the wooden beam
-
at the base:
𝜎𝑡2𝑑
𝑓𝑡0𝑑
+
𝜎𝑚2𝑑
𝑓𝑚𝑑
=
0,458
7,38
2,679
+ 12,46 = 0,277 ≤ 1
6.6.Verification of tangential stresses
ℎ2
250
− 𝑎2 =
− 21,35 = 146,35 𝑚𝑚
2
2
0,5 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝑏2 × ℎ2 × 𝑉𝐸𝑑
𝜏𝑚𝑎𝑥 =
≤ 𝑓𝑣𝑑
𝑏2 × (𝐸𝐼)𝑒𝑓
0,5 × 8144 × 190 × 146,352 × 9,3 × 103
=
= 0,229 ≤ 𝑓𝑣𝑑 = 1,29
190 × 3,53 × 1012
ℎ=
𝜏𝑚𝑎𝑥
7. Verification of cambers in the initial stage
The formulas given in Point 5 shall be used, introducing the moduli of elasticity for wood
Emean and concrete Ecm and the modulus of sliding Kser for connectors.
7.1. Characteristics of the composite section
45
(𝐸𝐼)𝑒𝑓 = (𝐸1 × 𝐼1 + 𝛾1 × 𝐸1 × 𝐴1 × 𝑎12 ) + (𝐸2 × 𝐼2 + 𝛾2 × 𝐸2 × 𝐴2 × 𝑎22 )
(𝐸𝐼)𝑒𝑓 = (31000 × 2,09 × 107 + 0,116 × 31000 × 39125 × 132,342 )
+ (12000 × 2,47 × 108 + 1 × 12000 × 47500 × 32,662 )
= 6,69 × 1012 𝑁𝑚𝑚2
𝛾1 =
1
1
=
= 0,116
2
3,14 × 31000 × 39125 × 117,5
𝜋 2 × 𝐸1 × 𝐴1 × 𝑠𝑒𝑓
1
+
1+
11520 × 40002
𝐾𝑠𝑒𝑟 × 𝑙 2
𝛾2 = 1
𝛾1 × 𝐸1 × 𝐴1 × (ℎ1 + ℎ2 )
2 × (𝛾1 × 𝐸1 × 𝐴1 + 𝛾2 × 𝐸2 × 𝐴2 )
0,116 × 31000 × 39125 × (80 + 250)
𝑎2 =
= 32,66 𝑚𝑚
2 × (0,116 × 31000 × 39125 + 1 × 12000 × 47500)
𝑎2 =
𝑎1 =
ℎ1 + ℎ2
80 + 250
− 𝑎2 =
− 32,66 = 132,34 𝑚𝑚
2
2
7.2.Calculation of camber
-
-
-
camber due to a permanent action
5 × 𝑔𝑑 × 𝑙 4
5 × 3145 × 10−3 × 40004
𝑤𝑖𝑛𝑠𝑡 𝐺 =
=
= 1,57 𝑚𝑚
384 × (𝐸𝐼)𝑒𝑓
384 × 6,69 × 1012
camber due to a variable (useful) action
5 × 𝑞𝑑 × 𝑙 4
5 × 1500 × 10−3 × 40004
𝑤𝑖𝑛𝑠𝑡 𝑄 =
=
= 0,748 𝑚𝑚
384 × (𝐸𝐼)𝑒𝑓
384 × 6,69 × 1012
instantaneous final camber
𝑙
𝑤𝑖𝑛𝑠𝑡 = 𝑤𝑖𝑛𝑠𝑡 𝐺 + 𝑤𝑖𝑛𝑠𝑡 𝑄 ≤ 𝑤𝑖𝑛𝑠𝑡,𝑎𝑑𝑚 =
300
4000
𝑤𝑖𝑛𝑠𝑡 = 1,57 + 0,748 = 2,32 𝑚𝑚 ≤ 𝑤𝑖𝑛𝑠𝑡 𝑎𝑑𝑚 =
= 13,3 𝑚𝑚
300
8. Verification of the camber at the SLE limit state in the final stage.
a. created by permanent actions: the deformations over time shall be taken into
consideration for all materials, as follows:
- Transformed modulus of elasticity of the wooden beams:
𝐸𝑚𝑒𝑎𝑛
12000
𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 =
=
= 9230 𝑁⁄𝑚𝑚2
1 + 𝛹 × 𝑘𝑑𝑒𝑓 1 + 0,5 × 0,6
- Modulus of sliding for the connection:
𝐾𝑠𝑒𝑟 = 0,08 × 𝑑 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 = 0,08 × 12 × 9230 = 8860 𝑁⁄
−- for the
𝑚𝑚 serviceabilit
𝑝𝑒𝑛𝑡𝑟𝑢 𝑆𝐿𝑆
y limit state
- Transformed modulus of elasticity of the concrete:
46
𝐸𝑐𝑚 𝑓𝑖𝑛 =
𝐸𝑐𝑚
31000
=
= 10333 𝑁⁄𝑚𝑚2
1 + 𝜑(∞, 𝑡0 ) 1 + 2,0
8.1.Characteristics of the composite section
(𝐸𝐼)𝑒𝑓 = (𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐼1 + 𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × 𝑎12 )
+ (𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐼2 + 𝛾2 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐴2 × 𝑎22 ) =
(𝐸𝐼)𝑒𝑓 = (10333 × 2,09 × 107 + 0,232 × 10333 × 39125 × 135,892 )
+ (9230 × 2,47 × 108 + 1 × 9230 × 47500 × 29,112 )
= 4,61 × 1012 𝑁𝑚𝑚2
1
1
𝛾1 =
=
= 0,232
2
2
3,14 × 10333 × 39125 × 117,5
𝜋 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × 𝑠𝑒𝑓
1+
1+
8860 × 40002
𝐾𝑠𝑒𝑟 × 𝑙 2
𝛾2 = 1
𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × (ℎ1 + ℎ2 )
𝑎2 =
=
2 × (𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 + 𝛾2 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐴2 )
0,232 × 10333 × 39125 × (80 + 250)
𝑎2 =
= 29,11 𝑚𝑚
2 × (0,232 × 10333 × 39125 + 1 × 9230 × 47500)
ℎ1 + ℎ2
80 + 250
𝑎1 =
− 𝑎2 =
− 29,11 = 135,89 𝑚𝑚
2
2
8.2.Calculation of camber:
- camber due to a permanent action
5 × 𝑔𝑑 × 𝑙 4
5 × 3145 × 10−3 × 40004
𝑤𝑓𝑖𝑛 𝐺 =
=
= 2,30 𝑚𝑚
384 × (𝐸𝐼)𝑒𝑓
384 × 4,61 × 1012
b. due to a variable action: the deformations over time shall be taken into consideration
for all materials, as follows:
- Transformed modulus of elasticity of the wooden beams:
𝐸𝑚𝑒𝑎𝑛
12000
𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 =
=
= 7500 𝑁⁄𝑚𝑚2
1 + 𝑘𝑑𝑒𝑓,𝑔 1 + 0,6
-
-
Modulus of sliding for the connection:
𝐾𝑠𝑒𝑟 = 0,08 × 𝑑 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 = 0,08 × 12 × 7500
= 6000 𝑁⁄
− 𝑝𝑒𝑛𝑡𝑟𝑢 𝑆𝐿𝑆
𝑚𝑚
Transformed modulus of elasticity of the concrete:
𝐸𝑐𝑚
31000
𝐸𝑐𝑚 𝑓𝑖𝑛 =
=
= 13777 𝑁⁄𝑚𝑚2
1 + 𝜑(∞, 𝑡0 )
1 + 1,25
8.3.Characteristics of the composite section
(𝐸𝐼)𝑒𝑓 = (𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐼1 + 𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × 𝑎12 )
+ (𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐼2 + 𝛾2 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐴2 × 𝑎22 )
47
- for the
serviceabilit
y limit state
(𝐸𝐼)𝑒𝑓 = (13777 × 2,09 × 107 + 0,1557 × 13777 × 39125 × 133,532 )
+ (7500 × 2,47 × 108 + 1 × 7500 × 47500 × 31,472 )
= 3,99 × 1012 𝑁𝑚𝑚2
1
𝛾1 =
1+
𝜋2
× 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × 𝑠𝑒𝑓
𝐾𝑠𝑒𝑟 × 𝑙 2
=
1+
3,142
1
= 0,1557
× 13777 × 39125 × 117,5
6000 × 40002
𝛾2 = 1
𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × (ℎ1 + ℎ2 )
𝑎2 =
2 × (𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 + 𝛾2 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐴2 )
0,1557 × 13777 × 39125 × (80 + 250)
𝑎2 =
= 31,47 𝑚𝑚
2 × (0,1557 × 13777 × 39125 + 1 × 7500 × 47500)
ℎ1 + ℎ2
80 + 250
𝑎1 =
− 𝑎2 =
− 31,47 = 133,53 𝑚𝑚
2
2
-
8.4.Calculation of cambers
camber due to a variable action
5 × 𝑞𝑑 × 𝑙 4
5 × 1500 × 10−3 × 40004
𝑤𝑓𝑖𝑛 𝑄 =
=
= 1,25 𝑚𝑚
384 × (𝐸𝐼)𝑒𝑓
384 × 3,99 × 1012
8.5.Final camber verification
𝑤𝑓𝑖𝑛
𝑙
𝑤𝑓𝑖𝑛 = 𝑤𝑓𝑖𝑛 𝐺 + 𝑤𝑓𝑖𝑛 𝑄 ≤ 𝑤𝑓𝑖𝑛,𝑎𝑑𝑚 =
200
4000
= 2,3 + 1,25 = 3,5 𝑚𝑚 ≤ 𝑤𝑓𝑖𝑛,𝑎𝑑𝑚 =
= 25 𝑚𝑚
200
9. Determination of the reinforcement required on the intermediary support
The calculation shall take into consideration a continuous beam with two openings. The
bending moment were determined by automatic calculation.
Hypothesis 1:
Hypothesis 2:
48
The area of reinforcement necessary in order to absorb the negative moment shall be
determined as for a rectangular concrete section, with the width b = 100 cm and the height h =
8 cm.
ℎ0 = ℎ − 𝑎𝑠 = 80 − 10 − 4 = 66 𝑚𝑚
4
𝑚 = 𝑀⁄
= 929 × 10 ⁄1000 × 662 × 14,45 = 0,147
𝑏 × ℎ02 × 𝑓𝑐𝑑
 percentage of reinforcement: p = 0.96 %
𝑝 × 𝑏 × ℎ0⁄
0,96 × 1000 × 66⁄
2
𝐴𝑠 =
100 =
100 = 633 𝑚𝑚
In accordance with Point 4.2(6) of the present guidelines:
𝐴𝑠 𝑚𝑖𝑛 = 0,4% × 𝐴𝑐 = 0,4 × 1000 × 80⁄100 = 320 𝑚𝑚2

The area required in order to absorb the negative moment: As = 633 mm2, resulting
8/8 cm.
10. Verification of the composite floor as a horizontal diaphragm
The elevation seismic force shall be determined in accordance with Chapter 3(7) of the
present guidelines, or by automatic calculation.
General data
Residential building with ground floor + 1 storey
Elevation height het = 2.90 m
Confined masonry structure, identical for the ground floor and 1st storey
The seismic area ag=0.16 g
Materials
- masonry elements: burnt clay solid bricks, fb = 7.5 N/mm2;
- M5 mortar;
- characteristic compressive strength of the masonry fk = 2.30 N/mm2 (CR 6, Table
4.2a, Fig.4.1b);
- characteristic shear strength with null unitary compressive stress of the masonry
fvk0 = 0.20 N/mm2 (CR 6, Table 4.3);
- longitudinal modulus of elasticity of the masonry Ez = 1 000 fk = 2.300 N/mm2 (CR
6, Table 4.9);
- transversal modulus of elasticity of the masonry Gz = 0.4Ez = 0.4 x 2 300 = 920
N/mm2 (CR 6, relationship 4.9).
Establishing the vertical loads
Total area of the storey:
9.05 x 9.05 = 81.91 m2
49
Net areas of the rooms: 2 x (4 x 5) + 3 x 8.8 = 66.4 m2
Areas occupied by the walls: 4 x (0.38 x 9.05) + 0.3 x 8.8 + 0.3 x 5.0 = 17.896 m2
17.896 x 2.90 = 51.90 m3
Masonry volume per storey:
Masonry weight:
volumetric weight of the masonry: γzid = 1.95 tonnes/m3 (including the
plastering)
total weight of the masonry: Gwall/ storey = 1.95 x 51.90 = 101.2 tonnes = 1012
kN
Floor weight:
8 cm reinforced concrete slab
flooring
separation walls
Operating load
qu
200 daN/m2
130 daN/m2
100 daN/m2
200 daN/m2
0.40
80 daN/m2
_______________
510 daN/m2
2i
2ix qu=200x0.40 =
Total weight per 1 m2 of floor
Total floor/storey weight:
66.4 x 510 = 33 864 daN = 33.86 tonnes
Total building/storey weight:
kN
Gnivel=101.2 x+ 33.86 = 135.06 tonnes = 1 350.6
qechiv = 135.06/81.91 = 1.64 tonnes/ m2 = 16.4
kN/m2
Total building weight:
G = 2 x 135.06 = 270.12 tonnes = 2 701.2 kN
The seismic force shall be calculated using the following coefficients:
for:
importance factor
I = 1.0
behaviour factor
q = 2.5 x 1.25 = 3.125
reduction factor
 = 0.88
value of the elastic design spectrum
Se = 0.16 g x 3.0
The sectional stresses in the floor were determined by automatic calculation.
Results obtained:
Normal tension in direction x:
𝑑𝑎𝑁
𝜎𝑥 = 5.5 𝑐𝑚2 = 0.55 𝑀𝑃𝑎
𝜎𝑥 < 𝑓𝑐𝑡𝑚 = 2.6 𝑀𝑃𝑎
50
y
x
Normal tension in direction y:
𝑑𝑎𝑁
𝜎𝑦 = 7.0 𝑐𝑚2 = 0.7 𝑀𝑃𝑎
𝜎𝑦 < 𝑓𝑐𝑡𝑚 = 2.6 𝑀𝑃𝑎
y
x
Displacement in direction z: 𝑑𝑟 = 0.497 𝑚𝑚
51
11. Construction and reinforcement of a timber-concrete composite floor
Beams made of solid coniferous wood shall be positioned at a distance b = 50 cm
(interax).
The connectors shall be distributed in a single row, inclined at 450, alternating
depending on the longitudinal section. The wood penetration depth of the threaded end of the
screw must be at least 60 mm.
Since the verification requirement for the stresses at the base of the concrete slab is
met, the constructive reinforcement stipulated in Point 4.2(4) shall be adopted – wire-tied net
8/200 x 8/200, installed 10 mm away from the base of the concrete slab.
The reinforcement mesh installed at the base shall be anchored in reinforced concrete
girdles along a length of 32 cm.
A mesh made of 8/8cm riders, distributed along the wooden beams and connected by
means of a 6/20 cm distribution reinforcement, shall be installed on the intermediary
support, at the top of the concrete slab, perpendicular to the riders.
12. Horizontal section and reinforcement details.
52
Longitudinal section through the wooden beam
1-1
Joint distribution area
Cross-section 2-2
Wooden beam distribution plan
Composite floor reinforcement plan
53
Example 2: Timber-concrete composite floor with one opening
This presents the design of an intermediary floor in a garage, with the planar
dimensions 8.75 x 6.75 metres and the elevation height het = 2.90 m. The load-bearing walls
are made of confined masonry with the thickness of 37.5 cm. The floor shall be built as a
timber-concrete composite system, using glued laminated beams.
Horizontal section
1:50 scale
Connection
distance between elements: s
modulus of sliding: K
stress: F
Note:
Timber-concrete composite section
54
1 - concrete slab
2 - wooden beam
3 - connector
The wooden beams shall be positioned in the short direction of the slab eyelet. The
distance between beams (interax) shall be chosen as follows:
𝑏 = 70 𝑐𝑚
Design of the composite floor
1. Characteristics of the chosen component materials
1.1. Wood – beams: beam made of homogenous glued laminated timber GL 28h;
operating Class 2.
Characteristic values – in accordance with SR EN 1995–1–1
- bending:
𝑓𝑚,𝑔,𝑘 = 28 𝑁⁄𝑚𝑚2
𝑓𝑡,0,𝑔,𝑘 = 19,5 𝑁⁄𝑚𝑚2
-
stretching along the fibre:
-
shearing:
𝑓𝑣,𝑔,𝑘 = 3,2 𝑁⁄𝑚𝑚2
-
modulus of elasticity:
𝐸𝑚𝑒𝑎𝑛 (𝐸2 ) = 12600 𝑁⁄𝑚𝑚2
-
density:
𝜌𝑔 ,𝑘 = 410
𝑘𝑔⁄
𝑚3
Partial certainty coefficients:
- coefficient that takes into account the effect of the load duration and humidity, in
accordance with SR EN 1995-1-1, Table 3.1., Note (2)
𝑘𝑚𝑜𝑑 = 0,80
-
coefficient for the material and strength, in accordance with SR EN 1995-1-1,
Table 2.3.
𝛾𝑀 = 1,25
-
coefficient which takes into account the deformations over time and the load
duration
𝑘𝑑𝑒𝑓,𝑝𝑒𝑟𝑚 = 0,60
𝑘𝑑𝑒𝑓,𝑚𝑒𝑑𝑖𝑒 = 0,60
Design values:
- bending:
-
𝑓𝑚,𝑑 =
k mod × fm,k
γM
𝑓𝑡,0,𝑑 =
stretching along the fibre:
=
0,80×28
1,25
= 17,92 𝑁⁄𝑚𝑚2
𝑘𝑚𝑜𝑑 × 𝑓𝑡,0,𝑘
𝛾𝑀
=
0,80 × 19,5
1,25
=
12,48 𝑁⁄𝑚𝑚2
-
shearing:
𝑓𝑣,𝑑 =
𝑘𝑚𝑜𝑑 × 𝑓𝑣,𝑘
𝛾𝑀
55
=
0,80 × 3,2
1,25
= 2,05 𝑁⁄𝑚𝑚2
1.2.Concrete – slab: Class C 25/30
Characteristic values: in accordance with SR EN 1992-1-1
- per cube:
𝑓𝑐,𝑘,𝑐𝑢𝑏𝑒 = 30 𝑁⁄𝑚𝑚2
- per cylinder:
𝑓𝑐,𝑘 = 25 𝑁⁄𝑚𝑚2
- mean value at axial tension: 𝑓𝑐,𝑡 = 2,6 𝑁⁄𝑚𝑚2
- modulus of elasticity:
𝐸𝑐,𝑚 (𝐸1 ) = 31000 𝑁⁄𝑚𝑚2
Partial certainty coefficients
- coefficient for the ultimate limit state, in accordance with SR EN 1992-1-1, Table
2.1.
1,5  permanenta, tranzitorie
Yc  
1,25  accidentala
- coefficients that take into account the long-term effect and unfavourable effects
resulting from the way in which the loads are applied
acc: (0.8 - 1) from SR EN 1992 – 1 – 1; acc = 0.85
act: recommended 1; act = 0.85
𝑘𝑡 = 0,85
Design values
- per cube:
𝑓𝑐,𝑑 =
-
𝑓𝑐,𝑡,𝑚𝑑 =
axial tension:
𝛼𝑐𝑐 × 𝑓𝑐𝑘,𝑐𝑢𝑏𝑒 × 𝑘𝑡
𝛾𝑐
𝛼𝑐𝑡 × 𝑓𝑐𝑡
𝛾𝑐
0,85×0,85×30
= 14,45 𝑁⁄𝑚𝑚2
0,85×2,60
= 1,5 = 1,47 𝑁⁄𝑚𝑚2
=
1,5
1.3.Connector
Type of connector: Screw
Diameter of connector: d=12 mm
Characteristic values:
- tension: 𝑓𝑢,𝑘 = 500 𝑁⁄𝑚𝑚2
-
modulus of sliding:
- for
𝐾𝑠𝑒𝑟 = 0,08 × 𝑑 × 𝐸𝑚𝑒𝑎𝑛 = 0,08 × 12 × 12600 = 12096
− the
𝑝𝑒𝑛𝑡𝑟𝑢 𝑆𝐿𝑆
serviceability
2
2
𝐾𝑢 = 3 𝐾𝑠𝑒𝑟 = 3 × 12096 = 8064 − 𝑝𝑒𝑛𝑡𝑟𝑢
- for the𝑆𝐿𝑈 limit state
ultimate limit
Partial certainty coefficients
state
- coefficient for connection (joining), in accordance with SR EN 1995-1-1, Table
2.3.
𝛾𝑀 = 1,3
-
coefficient which takes into account the deformations over time and the load
duration
𝑘𝑑𝑒𝑓,𝑝𝑒𝑟𝑚 = 0,60
𝑘𝑑𝑒𝑓,𝑚𝑒𝑑𝑖𝑒 = 0,60
56
2. Geometric characteristics of the chosen components
2.1.Wooden beam
- width:
𝑏2 = 120 𝑚𝑚
- height:
ℎ2 = 500 𝑚𝑚
-
𝐼2 =
𝑏2 ×ℎ23
=
120×5003
= 1,25 × 109 𝑚𝑚4
-
moment of inertia:
-
area:
𝐴2 = 𝑏2 × ℎ2 = 120 × 500 = 60000 𝑚𝑚2
span:
𝐿 = 6000 𝑚𝑚
distance between the beams (interax): 𝑏 = 700 𝑚𝑚
12
12
2.2.Concrete slab
thickness:
ℎ1 = 90 𝑚𝑚
- connection width calculated for evenly distributed loads in accordance with
relationship 3–3:
2
2
𝑏𝑒𝑓 = [1 − 1,4 × (𝑏⁄𝐿) ] × 𝑏 = [1 − 1,4 × (700⁄6000) ] × 700 = 687 𝑚𝑚
𝑏𝑒𝑓 ×ℎ13
= 4,17 × 107 𝑚𝑚4
moment of inertia:
𝐼1 =
-
area:
𝐴1 = 𝑏𝑒𝑓 × ℎ1 = 687 × 90 = 61800 𝑚𝑚2
12
=
687×903
-
12
2.3.Slab thickness verification:
𝐸1 × 𝐼1 31000 × 4,17 × 107
=
= 0,08 ≤ 1
𝐸2 × 𝐼2 12600 × 1,25 × 109
3. Loads and stresses.
3.1.Characteristic values, partial certainty coefficients, and design values
Permanent
Type of load
Net weight of the
reinforced concrete
slab
Flooring
Light partition walls
Net weight of the
wooden beams
Net
Characteristics
Partial
certainty
coefficient
Calculation
2250 𝑁⁄
𝑚2
1.35
3037,5 𝑁⁄
𝑚2
1300 𝑁⁄
𝑚2
1000 𝑁⁄
𝑚2
1.35
1755 𝑁⁄
𝑚2
1350 𝑁⁄
𝑚2
442 𝑁⁄
𝑚
2000 𝑁⁄
𝑚2
1.35
1.35
1.50
597 𝑁⁄
𝑚
3000 𝑁⁄
𝑚2
3.2.Linear stresses
- Permanent load:
𝑔𝑑 = (3037 + 1755 + 1350) × 0,700 + 597 = 4816 𝑁⁄𝑚
-
Net load
57
𝑞𝑑 = 3000 × 0,700 = 2100 𝑁⁄𝑚
3.3.Sectional stresses
-
Bending moment: 𝑀𝐸𝑑 =
-
Shear force: 𝑉𝐸𝑑 =
(𝑔𝑑 +𝑞𝑑 )×𝐿2
(𝑔𝑑 +𝑞𝑑 )×𝐿
2
8
=
=
(4,816+2,10)×60002
8
(4,816+2,10)×6000
2
= 30,9 × 106 𝑁𝑚𝑚
= 20,6 × 103 𝑁
4. Joint verification
4.1.Plastic moment of the connectors
𝑀𝑦,𝑘 0,583 × 𝑓𝑢,𝑘 × 𝑑 3
0,583 × 500 × 123
𝑀𝑦,𝑑 =
=
=
= 6,46 × 104 𝑁𝑚𝑚
𝛾𝑀
6 × 𝛾𝑀
6 × 1,3
4.2.Connection strength upon yielding of the concrete
𝑓𝑐,𝑘 × 𝐸𝑐𝑚
25 × 31000
𝑅𝑑 = 0,23 × 𝑑2 × √
= 0,23 × 122 × √
= 26078,71 𝑁
𝛾𝑐
1,25
4.3.Connection strength upon shearing rupture
𝑓𝑢,𝑘 × 𝜋 × 𝑑 2
500 × 3,14 × 122
𝑅𝑑 = 0,8 ×
= 0,8 ×
= 36172,8 𝑁
4 × 𝛾𝑐
4 × 1,25
4.4.Strength upon yielding of the wood
𝑅𝑑 = 1,5 × √2 × 𝑀𝑦𝑑 × 𝑓ℎ,2,𝑑 × 𝑑 = 1,5 × √2 × 6,46 × 104 × 18,93 × 12 = 8,13 × 103 𝑁
where:
𝑓ℎ,2,𝑘 = 0,082 × (1 − 0,01 × 𝑑) × 𝜌𝑘 = 0,082 × (1 − 0,01 × 12) × 410
= 29,58 𝑁⁄𝑚𝑚2
One shall introduce: ρk in kg 3 and d in mm, respectively
m
𝑘𝑚𝑜𝑑 × 𝑓ℎ,2,𝑘 0,8 × 29,58
𝑓ℎ,2,𝑑 =
=
= 18,93 𝑁⁄𝑚𝑚2
𝛾𝑀
1,25
5. Verification of stresses at the ultimate limit state in the initial stage.
5.1.Characteristics of the composite section
(𝐸𝐼)𝑒𝑓 = (𝐸1 × 𝐼1 + 𝛾1 × 𝐸1 × 𝐴1 × 𝑎12 ) + (𝐸2 × 𝐼2 + 𝛾2 × 𝐸2 × 𝐴2 × 𝑎22 )
= (31000 × 4,17 × 107 + 0,09 × 31000 × 61800 × 240,442 ) + 12600
× 1,25 × 109 + 1 × 12600 × 60000 × 54,562 = 2,92 × 1013 𝑁𝑚𝑚2
1
1
𝛾1 =
=
= 0,09
2
2
3,14 × 31000 × 61800 × 156,25
𝜋 × 𝐸1 × 𝐴1 × 𝑠𝑒𝑓
1+
1+
8064 × 60002
𝐾𝑢 × 𝐿2
𝛾2 = 1
𝑠𝑒𝑓 = 0,75 × 𝑠𝑚𝑖𝑛 + 0,25 × 𝑠𝑚𝑎𝑥 = 0,75 × 125 + 0,25 × 250 = 156,25 𝑚𝑚
𝛾1 × 𝐸1 × 𝐴1 × (ℎ1 + ℎ2 )
𝑎2 =
2 × (𝛾1 × 𝐸1 × 𝐴1 + 𝛾2 × 𝐸2 × 𝐴2 )
0,09 × 31000 × 61800 × (90 + 500)
=
= 54,56 𝑚𝑚
2 × (0,09 × 31000 × 61800 + 1 × 12600 × 60000)
58
𝑎1 =
ℎ1 + ℎ2
90 + 500
− 𝑎2 =
− 54,56 = 240,44 𝑚𝑚
2
2
5.2.Stresses in the concrete slab
𝛾1 × 𝐸1 × 𝑎1 × 𝑀𝐸𝑑 0,09 × 31000 × 240,44 × 30,9 × 106
𝜎𝑐,1,𝑑 =
=
= 0,71 𝑁⁄𝑚𝑚2
(𝐸𝐼)𝑒𝑓
2,92 × 1013
0,5 × 𝐸1 × ℎ1 × 𝑀𝐸𝑑 0,5 × 31000 × 90 × 30,9 × 106
𝜎𝑚,1,𝑑 =
=
= 1,48 𝑁⁄𝑚𝑚2
(𝐸𝐼)𝑒𝑓
2,92 × 1013
5.3.Verification of stresses in the concrete slab
- at the top: 𝜎𝑐,𝑑 = 𝜎𝑐,1,𝑑 + 𝜎𝑚,1,𝑑 = 0,71 + 1,48 = 2,18 ≤ 𝑓𝑐,𝑑 = 14,45
- at the base: 𝜎𝑡,𝑑 = 𝜎𝑚,1,𝑑 − 𝜎𝑐,1,𝑑 = 1,48 − 0,71 = 0,77 ≤ 𝑓𝑐,𝑡,𝑚,𝑑 = 1,47
5.4.Stresses in the wooden beam
𝛾2 × 𝐸2 × 𝑎2 × 𝑀𝐸𝑑 1 × 12600 × 54,56 × 30,9 × 106
𝜎𝑡,2,𝑑 =
=
= 0,73 𝑁⁄𝑚𝑚2
(𝐸𝐼)𝑒𝑓
2,92 × 1013
0,5 × 𝐸2 × ℎ2 × 𝑀𝐸𝑑 0,5 × 12600 × 500 × 30,9 × 106
𝜎𝑚,2,𝑑 =
=
= 3,34 𝑁⁄𝑚𝑚2
(𝐸𝐼)𝑒𝑓
2,92 × 1013
5.5.Verification of stresses in the wooden beam
-
at the base:
𝜎𝑡,2,𝑑
𝑓𝑡,0,𝑑
+
𝜎𝑚,2,𝑑
𝑓𝑚𝑑
=
0,73
3,34
+ 17,92 = 0,395 ≤ 1
12,48
5.6.Verification of tangential stresses
ℎ2
500
ℎ=
+ 𝑎2 =
+ 54,56 = 304,56 𝑚𝑚
2
2
0,5 × 𝐸2 × 𝑏2 × ℎ × 𝑉𝐸𝑑
𝜏𝑚𝑎𝑥 =
≤ 𝑓𝑣,𝑔,𝑑
𝑏2 × (𝐸𝐼)𝑒𝑓
𝜏𝑚𝑎𝑥
0,5 × 12600 × 120 × 304,56 × 20,6 × 103
=
= 0,0014 ≤ 2,05 𝑁⁄𝑚𝑚2
120 × 2,92 × 1013
5.7.Verification of stresses in the connectors
𝛾1 × 𝐸1 × 𝐴1 × 𝑎1 × 𝑠𝑚𝑖𝑛 × 𝑉𝐸𝑑
𝐹1,𝑑 =
≤ min(R d )
(𝐸𝐼)𝑒𝑓
𝐹1,𝑑 =
0,09 × 31000 × 61800 × 240,44 × 125 × 20,6 × 103
= 3641,64 ≤ 8125,89 N
2,92 × 1013
6. Verification of stresses at the ultimate limit state in the final stage.
The deformations over time shall be taken into consideration for all materials, as follows:
- Transformed modulus of elasticity of the wooden beams:
59
%𝐺
%𝑄
0,70
0,30
𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 = 𝐸𝑚𝑒𝑎𝑛 × (
+
) = 12600 × (
+
)
1 + 𝛹 × 𝑘𝑑𝑒𝑓 1 + 𝑘𝑑𝑒𝑓
1 + 0,60 1 + 0,6
= 7875 𝑁⁄𝑚𝑚2
- Modulus of sliding for the connection:
for𝑝𝑒𝑛𝑡𝑟𝑢
the
𝐾𝑠𝑒𝑟 = 0,08 × 𝑑 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 = 0,08 × 12 × 7875 = 7560- −
𝑆𝐿𝑆
serviceability
2
2
𝐾𝑢 = 3 𝐾𝑠𝑒𝑟 = 3 × 7560 = 5040 − -𝑝𝑒𝑛𝑡𝑟𝑢
for the 𝑆𝐿𝑈
limit state
ultimate
limit
- Transformed modulus of elasticity of the concrete:
state
1
0,70
𝐸𝑐𝑚 𝑓𝑖𝑛 = 𝐸𝑐𝑚 × (
) = 31000 × (
) = 10634 𝑁⁄𝑚𝑚2
1 + 𝜑(∞, 𝑡0 )
1 + 3.25
6.1.Characteristics of the composite section
(𝐸𝐼)𝑒𝑓 = (𝐸1,𝑡 × 𝐼1 + 𝛾1 × 𝐸1,𝑡 × 𝐴1 × 𝑎12 ) + (𝐸2,𝑡 × 𝐼2 + 𝛾2 × 𝐸2,𝑡 × 𝐴2 × 𝑎22 )
= (10634 × 4,17 × 107 + 0,152 × 10634 × 61800 × 243,522 )
+ (7875 × 1,25 × 109 + 1 × 7875 × 60000 × 51,482 )
= 1,75 × 1013 𝑁𝑚𝑚2
1
1
𝛾1 =
=
= 0,152
2
2
3,14 × 10634 × 61800 × 156,25
𝜋 × 𝐸1,𝑡 × 𝐴1 × 𝑠𝑒𝑓
1+
1+
5040 × 60002
𝐾𝑢 × 𝐿2
𝛾2 = 1
𝛾1 × 𝐸1,𝑡 × 𝐴1 × (ℎ1 + ℎ2 )
𝑎2 =
2 × (𝛾1 × 𝐸1,𝑡 × 𝐴1 + 𝛾2 × 𝐸2,𝑡 × 𝐴2 )
0,152 × 10634 × 61800 × (90 + 500)
𝑎2 =
= 51,48 𝑚𝑚
2 × (0,152 × 10634 × 61800 + 1 × 7875 × 60000)
ℎ1 + ℎ2
90 + 500
𝑎1 =
− 𝑎2 =
− 51,48 = 243,52 𝑚𝑚
2
2
6.2.Stresses in the concrete slab
𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝑎1 × 𝑀𝐸𝑑
0,152 × 10634 × 243,52 × 30,9 × 106
𝜎𝑐,1,𝑑 =
=
(𝐸𝐼)𝑒𝑓
1,75 × 1013
= 0,697 𝑁⁄𝑚𝑚2
0,5 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × ℎ1 × 𝑀𝐸𝑑 0,5 × 10634 × 90 × 30,9 × 106
𝜎𝑚,1,𝑑 =
=
(𝐸𝐼)𝑒𝑓
1,75 × 1013
= 0,848 𝑁⁄𝑚𝑚2
6.3.Verification of stresses in the concrete slab
- at the top: 𝜎𝑐,𝑑 = 𝜎𝑐,1,𝑑 + 𝜎𝑚,1,𝑑 = 0,697 + 0,848 = 1,546 ≤ 𝑓𝑐,𝑑 = 14,45
- at the base: 𝜎𝑡,𝑑 = 𝜎𝑚,1,𝑑 − 𝜎𝑐,1,𝑑 = 0,848 − 0,697 = 0,151 ≤ 𝑓𝑐,𝑡,𝑚,𝑑 = 1,47
6.4.Stresses in the wooden beam
60
𝜎𝑡,2,𝑑
𝜎𝑚,2,𝑑
𝛾2 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝑎2 × 𝑀𝐸𝑑 1 × 7875 × 51,48 × 30,9 × 106
=
=
(𝐸𝐼)𝑒𝑓
1,75 × 1013
= 0,718 𝑁⁄𝑚𝑚2
0,5 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × ℎ2 × 𝑀𝐸𝑑 0,5 × 7875 × 500 × 30,9 × 106
=
=
(𝐸𝐼)𝑒𝑓
1,75 × 1013
= 3,489 𝑁⁄𝑚𝑚2
6.5.Verification of stresses in the wooden beam
-
at the base:
𝜎𝑡,2,𝑑
𝑓𝑡,0,𝑑
+
𝜎𝑚,2,𝑑
𝑓𝑚𝑑
=
0,718
12,48
3,489
+ 17,92 = 0,252
≤ 1
7. Verification of deformations at the SLE limit state in the initial stage
7.1.Characteristics of the composite section
(𝐸𝐼)𝑒𝑓 = (𝐸1 × 𝐼1 + 𝛾1 × 𝐸1 × 𝐴1 × 𝑎12 ) + (𝐸2 × 𝐼2 + 𝛾2 × 𝐸2 × 𝐴2 × 𝑎22 )
(𝐸𝐼)𝑒𝑓 = (31000 × 4,17 × 107 + 0,129 × 31000 × 61800 × 222,502 ) + (12600
× 1,25 × 106 + 1 × 12600 × 60000 × 72,502 ) = 3,32 × 1013 𝑁𝑚𝑚2
1
1
𝛾1 =
=
= 0,129
2
2
3,14 × 31000 × 61800 × 156,25
𝜋 × 𝐸1 × 𝐴1 × 𝑠𝑒𝑓
1
+
1+
12096 × 60002
𝐾𝑠𝑒𝑟 × 𝐿2
𝛾2 = 1
𝛾1 × 𝐸1 × 𝐴1 × (ℎ1 + ℎ2 )
𝑎2 =
2 × (𝛾1 × 𝐸1 × 𝐴1 + 𝛾2 × 𝐸2 × 𝐴2 )
0,129 × 31000 × 61800 × (90 + 500)
𝑎2 =
= 72,50 𝑚𝑚
2 × (0,129 × 31000 × 61800 + 1 × 12600 × 60000)
ℎ1 + ℎ2
90 + 500
𝑎1 =
− 𝑎2 =
− 72,50 = 222,50 𝑚𝑚
2
2
7.2.Calculation of camber
- camber due to a permanent action
5 × 𝑔𝑑 × 𝐿4
5 × 4816 × 10−3 × 60004
𝑤𝑖𝑛𝑠𝑡,𝑔 =
=
= 2,45𝑚𝑚
384 × (𝐸𝐼)𝑒𝑓
384 × 3,32 × 1013
- camber due to an average-duration action
5 × 𝑞𝑑 × 𝐿4
5 × 2061 × 10−3 × 60004
𝑤𝑖𝑛𝑠𝑡,𝑞 =
=
= 1,05𝑚𝑚
384 × (𝐸𝐼)𝑒𝑓
384 × 3,32 × 1013
- instantaneous, final camber
𝐿
𝑤𝑖𝑛𝑠𝑡 = 𝑤𝑖𝑛𝑠𝑡,𝑔 + 𝑤𝑖𝑛𝑠𝑡,𝑞 = ≤ 𝑤𝑖𝑛𝑠𝑡,𝑎𝑑𝑚 =
300
6000
𝑤𝑖𝑛𝑠𝑡 = 2,45 + 1,05 = 3,49 ≤ 𝑤𝑖𝑛𝑠𝑡,𝑎𝑑𝑚 =
= 20
300
8. Calculation of deformations at the SLE in the final stage, due to permanent
actions
The deformations over time shall be taken into consideration for all materials, as follows:
- Transformed modulus of elasticity of the wooden beams:
61
𝐸𝑚𝑒𝑎𝑛
12600
=
= 7875 𝑁⁄𝑚𝑚2
1 + 𝛹 × 𝑘𝑑𝑒𝑓 1 + 0,6
Modulus of sliding for the connection:
for𝑝𝑒𝑛𝑡𝑟𝑢
the
𝐾𝑠𝑒𝑟 = 0,08 × 𝑑 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 = 0,08 × 12 × 7875 = 7560- −
𝑆𝐿𝑆
serviceability
Transformed modulus of elasticity of the concrete:
limit state
𝐸𝑐𝑚
31000
𝑁
𝐸𝑐𝑚 𝑓𝑖𝑛 =
=
= 9538 ⁄𝑚𝑚2
1 + 𝜑(∞, 𝑡0) 1 + 2,25
𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 =
-
8.1.Characteristics of the composite section
(𝐸𝐼)𝑒𝑓 = (𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐼1 + 𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × 𝑎12 )
+ (𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐼2 + 𝛾2 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐴2 × 𝑎22 ) =
(𝐸𝐼)𝑒𝑓 = (9538 × 4,17 × 107 + 0,231 × 9538 × 61800 × 229,12 ) + (7875 × 1,25
× 109 + 1 × 7875 × 60000 × 65,92 ) = 1,94 × 1013 𝑁𝑚𝑚2
1
1
𝛾1 =
=
= 0,231
2
2
3,14 × 9538 × 61800 × 156,25
𝜋 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × 𝑠𝑒𝑓
1+
1+
7560 × 60002
𝐾𝑠𝑒𝑟 × 𝐿2
𝛾2 = 1
𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × (ℎ1 + ℎ2 )
𝑎2 =
=
2 × (𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 + 𝛾2 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐴2 )
0,231 × 9538 × 61800 × (90 + 500)
𝑎2 =
= 65,90 𝑚𝑚
2 × (0,231 × 9538 × 61800 + 1 × 7875 × 60000)
ℎ1 + ℎ2
60 + 500
𝑎1 =
− 𝑎2 =
− 65,90 = 229,10 𝑚𝑚
2
2
8.2.Calculation of camber:
- camber due to a permanent action
5 × 𝑔𝑑 × 𝐿4
5 × 4816 × 10−3 × 60004
𝑤𝑓𝑖𝑛 𝐺 =
=
= 4,2 𝑚𝑚
384 × (𝐸𝐼)𝑒𝑓
384 × 1,94 × 1013
9. Calculation of deformations at the SLE in the final stage, due to averageduration actions
The deformations over time shall be taken into consideration for all materials, as follows:
- Transformed modulus of elasticity of the wooden beams:
𝐸𝑚𝑒𝑎𝑛
12600
𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 =
=
= 7875 𝑁⁄𝑚𝑚2
1 + 𝛹 × 𝑘𝑑𝑒𝑓 1 + 0,6
-
Modulus of sliding for the connection:
for𝑝𝑒𝑛𝑡𝑟𝑢
the 𝑆𝐿𝑆
𝐾𝑠𝑒𝑟 = 0,08 × 𝑑 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 = 0,08 × 12 × 7875 = 7560-−
serviceability
- Transformed modulus of elasticity of the concrete:
limit state
𝐸𝑐𝑚
31000
𝑁
𝐸𝑐𝑚 𝑓𝑖𝑛 =
=
= 13191 ⁄𝑚𝑚2
1 + 𝜑(∞, 𝑡0)
1 + 1,35
9.1.Characteristics of the composite section
(𝐸𝐼)𝑒𝑓 = (𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐼1 + 𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × 𝑎12 )
+ (𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐼2 + 𝛾2 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐴2 × 𝑎22 )
62
(𝐸𝐼)𝑒𝑓 = (13191 × 4,17 × 107 + 0,1781 × 13191 × 61800 × 225,662 ) + (7875
× 1,25 × 109 + 1 × 7875 × 60000 × 69,342 ) = 2,01 × 1013 𝑁𝑚𝑚2
1
𝛾1 =
1+
𝜋2
× 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × 𝑠𝑒𝑓
𝐾𝑠𝑒𝑟 × 𝐿2
=
1+
3,142
1
= 0,1781
× 13191 × 61800 × 156,25
7560 × 60002
𝛾2 = 1
𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 × (ℎ1 + ℎ2 )
𝑎2 =
2 × (𝛾1 × 𝐸𝑐𝑚 𝑓𝑖𝑛 × 𝐴1 + 𝛾2 × 𝐸𝑚𝑒𝑎𝑛 𝑓𝑖𝑛 × 𝐴2 )
0,1781 × 13191 × 61800 × (90 + 500)
𝑎2 =
= 69,34 𝑚𝑚
2 × (0,1781 × 13191 × 61800 + 1 × 7875 × 60000)
ℎ1 + ℎ2
90 + 500
− 𝑎2 =
− 69,34 = 225,66 𝑚𝑚
2
2
9.2.Calculation of camber:
- camber due to an average-duration action
5 × 𝑞𝑑 × 𝐿4
5 × 2061 × 10−3 × 60004
𝑤𝑓𝑖𝑛 𝑄 =
=
= 1,7𝑚𝑚
384 × (𝐸𝐼)𝑒𝑓
384 × 2,01 × 1013
𝑎1 =
9.3.Final camber verification
𝑤𝑓𝑖𝑛
𝐿
𝑤𝑓𝑖𝑛 = 𝑤𝑓𝑖𝑛 𝐺 + 𝑤𝑓𝑖𝑛 𝑄 = ≤ 𝑤𝑓𝑖𝑛,𝑎𝑑𝑚 =
200
6000
= 4,2 + 1,7 = 5,9 ≤ 𝑤𝑓𝑖𝑛,𝑎𝑑𝑚 =
= 30 𝑚𝑚
200
10. Construction and reinforcement of a timber-concrete composite floor.
Beams made of glued laminated timber shall be positioned at a distance b = 70 cm
(interax).
The connectors shall be distributed in a single row, inclined at 450, alternating
depending on the longitudinal section. The wood penetration depth of the threaded end of the
screw must be at least 72 mm.
Since the verification requirement for the stresses at the base of the concrete slab is
met, the constructive reinforcement stipulated in Point 4.2(4) shall be adopted – wire-tied net
8/200 x 8/200, installed at the base of the concrete slab
The reinforcement mesh shall be anchored in reinforced concrete girdles along a
length of 32 cm.
11. Horizontal section and distribution and reinforcement details.
Composite floor distribution and
reinforcement plan
1:50 scale
63
1
1-1
2
1
2-2
64
2
Longitudinal section through the wooden beam
Joint distribution area
Cross-section
65