Fastening plate design
Peikko Group
FASTENING PLATE CALCULATIONS
Date:
26th Oct 2017
Fastening plate design
CONTENT:
1. General
1.1Applied Standards
1.2Materials
1.3Safety Factors
1.4Load Combinations
1.5Enviromental Conditions
2. Dimensions
3. Design of Plates
3.1 Steel strength in tension
3.2 Concrete breakout strength in tension
3.3 Pullout strength
3.4 Steel strength in shear
3.5 Pryout strength
3.6 Concrete breakout strength in shear
3.7 Interaction strength
3.8 Plate bending strength
4. Results
Peikko Group
Fastening plate design
1
Peikko Group
GENERAL
Fastening plates for Wylfa Nuclear project.
Connection will be welded connection between the structures.
1.1
APPLIED STANDARDS
Loading combinations should follow ASCE7-10
Design of base plates shall be by AISC 360-10 LRFD
Design of anchor bolts shall be by ACI 318M-2011 Appendix-D
1.2
MATERIALS
EN 10025-2:2004– Hot rolled structural steel, non-alloy quality steel,
for general purpose.
S355J2+N - Plate
EN ISO-13918 – Welding Studs and Ceramic Ferrules for Arc Stud Welding
ISO/TR15608 – Welding Guidelines for Metallic Materials Grouping System
Headed Studs – SD1 (fy=350MPa; fu=450MPa)
ACI318M-11 – Building Code Requirements for Structural Concrete
Minimum compressive strength of concrete – 35 mPa (Cylinder)
Minimum compressive strength of concrete – 45 mPa (Cube)
1.3
SAFETY FACTORS
Safety factors for different materials as listed below:
Plate
Yield strength
Tensile strength
Safety factor
S355
fy
fu
Ø
355 MPa
500 MPa
0.9
Fastening plate design
Studs
Yield strength
Tensile strength
Modulus of elasticity
Safety factor - tension
Safety factor - shear
Concrete
Compressive strength
Maximum strain
Safety factor
Safety factor
1.4
Peikko Group
ISO/TR 15608
SD1
fy
350 MPa
fu
450 MPa
Es
200000 MPa
Ø
0.75
Ø
0.65
fc'
εc
Ø
Ø
35 MPa
0.003
0.75
0.7
(Condition A –ACI318M-11)
(Pullout&Pryout)
LOAD COMBINATIONS
Loading combinations should follow ASCE 7-10 and ACI318M-11 instructions for the
applicable loading cases.
ULS factored loading combinations should be compared to the LRFD capacities of the
fastening plates.
Capacities has been designed as per static loads, in case of seismic or dynamic loads
additional requirements in ACI 318M-11 should be considered.
1.5
ENVIROMENTAL CONDITIONS
Corrosion and fire resistance hasn’t been considered in the calculations.
This should be taken into account according to the project requirements.
2 DIMENSIONS
Fastening plate dimensions are following the Figure 1 instructions.
Fastening plate design
Peikko Group
Figure 1. Fastening plate dimensions
3 DESIGN OF PLATES
Strengths in different cases has been calculated in chapters 3.1 – 3.8.
In these strengths additional reinforcement hasn’t been taken into account but concrete
strengths can be increased by adding additional reinforcement.
3.1 Steel strength of anchors in tension
Steel strength of single anchor can be obtained as follows:
Where
Ase
fy
=
= Cross-section area of stud
= Yield strength of the stud
∙
Steel strength of group of anchors can be obtained as follows:
Fastening plate design
Where
Ø
n
Peikko Group
∅
=∅∙
= Safety factor of stud
= number of studs
∙
3.2 Concrete breakout strength in tension
Concrete breakout strength is calculated for anchors in tension. All the anchors has been
expected to be loaded equally with tension force. Concrete edge distance has not been
considered and it should be > 1.5 ∙ ℎ .
Concrete breakout strength for group of anchors can be obtained as follows:
Where
ANc
ANco
Ψec,N
E’n
Ψed,N
Ψc,N
Nb
hef
fc’
kc
∅
=
∙
∙
,
,
∙
,
∙
= Total projected area = (3ℎ + ) ∙ (3ℎ + )
= Maximum projected area of single anchor = 9ℎ
= Factor for eccentricity =
= Eccentricity of load
= Factor for concrete edge effect = > 1.5ℎ
= Factor for concrete cracking = 1.0 (cracked concrete)
= Basic concrete breakout strength = ∙
∙ℎ .
= Effective anchor height
= Concrete grade
= Factor for anchors = 10 (cast-in anchors)
3.3 Pullout strength
Pullout strength of single anchor can be obtained as follows:
Where
Ψc,p
Np
Abrg
=
,
∙
= Factor for concrete cracking = 1.0 (cracked concrete)
= Pullout strength = 8 ∙
∙
= Cross-section of the head with shaft excluded
Fastening plate design
Peikko Group
Pullout strength of group of anchors can be obtained as follows:
Where
Ø
∅
=∅∙
∙
= Safety factor for concrete in pullout
3.4 Steel strength of anchors in shear
Steel strength for the single anchor in shear can be obtained as follows:
= 0.6 ∙
∙
Steel strength for group of anchors in shear can be obtained as follows:
Where
Ø
∅
=∅∙
∙
= Safety factor of stud in shear
3.5 Pryout strength of anchors
Pryout strength of the anchor can be obtained as follows:
Where
kcp
Ncbg
Ø
∅
=∅∙
∙
= Pryout factor for anchors = 2 (if h ef ≥65mm)
= Concrete breakout strength (see chapter 3.2)
= Safety factor for pryout
3.6 Concrete breakout strength for shear
Embedded plates has been assumed to be in the middle of the structure where edge
distance is not limiting the capacity due to his concrete breakout strength in shear will not
govern the calculation and can be ignored.
Fastening plate design
Peikko Group
3.7 Interaction strength
Interaction strength is applied as per ACI318M-11 trilinear approach as shown in Figure
2 below:
If
If
If
∅
∅
∅
≤ 0.2 full strength in tension shall be permitted
≤ 0.2 full strength in shear shall be permitted
> 0.2 for the governing strength in shear and
in tension then:
∅
+
∅
∅
> 0.2 for the governing strength
≤ 1.2
Figure 2. Trilinear approach
where
ØNn = MIN (Nsag;Ncbg;Npng)
ØV n = MIN (Vsag;Vcpg)
3.8 Plate bending strength
Plate bending resistance is based on the assumed yield line distance from the anchors.
Yield line will occur in the side of the profile.
Fastening plate design
Peikko Group
Yield line can occur either parallel to L and B dimensions in that case 2 or more bolts
will cause the bending for the plate or it can be from the corner in that case 1 bolt will
cause the bending of the plate.
Yield line theories and dimensions are shown in Figure 3.
Figure 3. Yield line theories
Distances x1;x2;x3 from the yield lines can be obtained as follows:
=
Where
h
s1
s2
=
=
−ℎ
2
−ℎ
2
−ℎ
2
+
−ℎ
2
= Attached profile size (square)
= Spacing of outermost studs parallel to L
= Spacing of outermost studs parallel to B
In case where the yield line occurs to the corner of the plate length of yield line can be
obtained as follows:
Where
L
B
= Plate length
= Plate width
=
2∙
−ℎ
2
+2∙
−ℎ
2
Fastening plate design
Peikko Group
Max tension force for single stud which plate is able to transfer can be obtained as
follows:
Where
t
fy
nL
nB
Ø
ØNsa
=
(
∙ ∙ ∙∅ ∙ ∙ ∙∅
;
;
4∙ ∙
4∙ ∙
∙
4∙
∙
∙∅
;∅
)
= Plate thickness
= Yield strength of plate
= Number of studs in row parallel to L
= Number of studs in row parallel to B
= Safety factor for plate
= Steel strength of stud (see chapter 3.1)
Max tension force for group of anchors which plate is able to transfer can be obtained as
follows:
∅
=
∙