Structural Engineering, I
Introduction to
Structural Analysis
Chapter 1
Contents
1.
Structural Engineering
2.
Structural Analysis
3.
Structural Elements
4.
Structural Systems
5.
Support Connections
6.
Structural Loads
7.
Structural Idealization
2
1.1 What is Structural Engineering?

a sub-division of civil engineering in which
structural engineers are trained to
understand, predict, and calculate the stability,
strength and rigidity of built structures for
buildings and non-building structures

For structural engineers to develop designs
and integrate their design with that of other
designers, and to supervise construction of
projects on site.
4
1.2 What is Structural Analysis?
Architectural
Plans
Structural
System
Conceptual
Design
5
Modelling
Detailing
Analysis
Member Design
Modelling &
Analysis
Design &
Detailing
Conceptual Design
Bedroom
12 m
Kitchen
Dining/Living
12 m
6
Garage
Ground Floor Plan
http://www.pinoyeplans.com/listing/modern-house-design-2012004/
Architectural Plans – Two Story Residence
Second Floor Plan
http://www.pinoyeplans.com/listing/modern-house-design-2012004/
Architectural Plans – Two Story Residence
Perspective View
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Architectural Plans – Two Story Residence
Structural System
3.5 m
2.0 m
2.5 m
3.0 m
3.5 m
3.5 m
where:
Columns
Beams
3.5 m
2.5 m
3.0 m
Second Floor Plan
Structural Modelling
Structural Analysis
12
Structural
Members
Applied
External Forces
Internal
Forces
Beams
Dead Load
Shear
Columns
Live Load
Moment
Slabs
Wind Load
Axial Force
Footings
Etc.
Reactions
Structural Analysis and Design
Structural Analysis

Calculation of
magnitudes of forces
and deformations
13
Structural Design

Arrangement and
proportioning of
structures and their
parts so as to
support their loads
adequately
Considerations of a Structural Engineer
Strength
 Safety
 Serviceability
 Economic Constraints
 Environmental Impact
 Aesthetics

14
Strength

Strength of a structure depends on the strength
of the materials from which it is made.

Strength of a material refers to the material's
ability to resist an applied force.

Strength is considered in terms of
 compressive strength
 tensile strength
 shear strength
 flexural strength, etc.
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15
Safety

Requires that the strength
of the structure be
adequate for all loads that
may foreseeably act on it.

Can be ensured by
providing
a
carrying
capacity just barely in
excess of the known loads.
16
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Serviceability
Pertains to the performance of structures under
normal service loads and is concerned with such
items as deflections, vibrations, cracking, and
slipping.
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Deflection
17
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Cracking
Spalling
Economy

Systematic evaluation of the
economic
merits
of
proposed
solutions
to
engineering problems.
Key issues:
 Time value of money
 Cash flows occurring at
different times
 “Designs” with different
18 durations

1.3 Structural Elements
19

Beams and Girders

Columns

Slabs/Diaphragms

Tie Rods/Bracing Struts
Source: Oreta, (2011)
20
Source: Oreta, (2011)
21
Source: Oreta, (2011)
22
1.4 Structural Systems
23

Frames

Surface structures

Arches

Cables

Trusses
Source: Oreta, (2011)
24
Source: Oreta, (2011)
25
Source: Oreta, (2011)
26
Source: Oreta, (2011)
27
Source: Oreta, (2011)
28
Source: Oreta, (2011)
29
Source: Oreta, (2011)
30
1.5 Support Connections
31

Fixed

Roller

Pin/Hinge

Link
Source: Oreta, (2011)
32
Source: Oreta, (2011)
33
Support Connections (Cont.)
Roller support
Link
34
Pin or hinge support
Support Connections (Cont.)
35
Support Connections (Cont.)
36
1.6 Structural Loads

The first phase of structural design consists of
estimating the loads acting on the structure.

The structure must be designed to carry or
resist loads that are applied to it over its
design-life. The loads have been categorized as
follows:
•
•
•
•
Dead Load (D)
• Impact Load (I)
Live Load (L)
• Hydrostatic and Soil Pressure (H)
Wind Load (W)
• Thermal Effects (T)
Earthquake Load (E)
37
Structural Loads (Cont.)
National Structural Code of the Philippines
(NSCP)
 ASEP Steel Handbook
 American Concrete Institute (ACI)
 American Society of Testing and Materials
(ASTM)
 American Association of State Highway and
Transportation Officials (AASHTO)

38
www.buildinghow.com
Dead Loads
◼
Permanent loads acting on
the structure
39
◼
Include the self-weight of
structural and non-structural
components
Dead Load
Consist of the weight of all materials of construction
incorporated into the building, including but not limited
to
Roof
Ceiling
40
Partition
Finishes
Cladding
Dead Load: Fixed Service Equipment
electricalinstallationwiringpicture.blogspot.com
• Electrical feeders
• Heating, ventilating
delafleur.com
conditioning systems
• Plumbing stacks and risers
41
and
air-
Dead Load (Cont.)

Can be estimated satisfactorily from simple
formulas based on the weights and sizes of
similar structures.

Once the materials and sizes of the various
components of the structure are determined,
their weights can be found from tables that list
their densities.

See Tables 204-1 and 204-2 of the NSCP, 2010.
42
Excerpt from Table 204-1. Minimum
Densities for Design Loads from Materials
(kN/m3)
Material
Concrete, Reinforced
Cinder
Slag
Stone, (including gravel)
43
Source: NSCP, 2015
Density (kN/m3)
17.4
21.7
23.6
Excerpt from Table 204-2. Minimum Design
Dead Loads (kPa)
Component
Floor fill
Cinder concrete, per mm
Lightweight concrete, per mm
Sand, per mm
Stone concrete, per mm
Ceilings
Suspended metal lath and cement plaster
Suspended metal lath and gypsum plaster
44
Source: NSCP, 2015
Load (kPa)
0.017
0.015
0.015
0.023
0.72
0.48
Example 1.1*
The second floor of a light manufacturing building is
constructed from a 125 mm thick stone concrete
slab with an added 100 mm cinder, concrete fill as
shown. If the suspended ceiling of the first floor
consists of metal lath and gypsum plaster, determine
the dead load for design in kPa of floor area.
45
*Problem 1-10, Hibbler. R. C., Structural Analysis, 8th Ed., p.28
Solution
46

Non-permanent loads
acting on the structure.

The magnitude and
location of live loads
changes frequently over
the design life.

They cannot be
estimated with the same
accuracy as dead loads.
47
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Live Loads
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Table 205-1. Minimum Uniform and
Concentrated Live Loads (NSCP, 2015)
Uniform
Load
Conc.
Load
kPa
kN
Office use
2.4
9.0
Computer use
4.8
9.0
3. Theaters, assembly areas Fixed seats
and auditoriums
Movable seats
Lobbies and
platforms
Stage areas
7.2
2.9
4.8
4.8
0
0
0
0
7.2
0
USE OR OCCUPANCY
Category
1. Access floor systems
2. Armories
48
Description
Table 205-1 (Continued)
Description
Uniform
Load
kPa
Conc.
Load
kN
-
3.6
0
-
1.9
1.3
-
3.6
0
-
4.8
0
-
4.8
0
USE OR OCCUPANCY
Category
4. Bowling alleys,
poolrooms and similar
recreational areas
5. Catwalk for maintenance
access
6. Cornices and marquees
7. Dining rooms and
restaurants
8. Exit facilities
49
Table 205-1 (Continued)
USE OR OCCUPANCY
Category
9. Parking
garages and
ramps
10. Hospitals
11. Libraries
50
Description
General storage/repair
Public parking
Private (residential) or
pleasure-type motor
vehicle storage
Wards and rooms
Laboratories & operating
rooms
Corridors above ground
floor
Reading rooms
Stack rooms
Uniform
Load
kPa
Conc.
Load
kN
4.8
2.4
-
2.4
-
1.9
4.5
2.9
4.5
3.8
4.5
2.9
7.2
4.5
4.5
Table 205-1 (Continued)
Uniform
Load
kPa
Conc.
Load
kN
Light
6.0
9.0
Heavy
12.0
13.4
Call centers & BPO
Lobbies and ground
floor corridors
Offices
2.9
9.0
4.8
9.0
2.4
9.0
USE OR OCCUPANCY
Category
12. Manufacturing
13. Office
51
Description
Table 205-1 (Continued)
Uniform
Load
Conc.
Load
kPa
kN
Press rooms
7.2
11.0
Composing & linotype
rooms
4.8
9.0
Basic floor area
Exterior balconies
Decks
Storage
1.9
2.9
1.9
1.9
0
0
0
0
-
-
USE OR OCCUPANCY
Category
14. Printing plants
15. Residential
16. Restrooms
52
Description
-
Table 205-1 (Continued)
Uniform
Load
Conc.
Load
Description
kPa
kN
-
4.8
0
18. Roof decks
Same as area served
or Occupancy
-
-
19. Schools
Classrooms
Corridors above
ground floor
Ground floor
corridors
1.9
4.5
3.8
4.5
4.8
4.5
USE OR OCCUPANCY
Category
17. Reviewing stands,
grandstands, bleachers,
folding & telescoping
seating
53
Table 205-1 (Continued)
Uniform
Load
Conc.
Load
Description
kPa
kN
20. Sidewalks &
driveways
Public access
12.0
-
21. Storage
Light
6.0
-
Heavy
12.0
-
Retail
Wholesale
4.8
6.0
4.5
13.4
4.8
-
USE OR OCCUPANCY
Category
22. Stores
23. Pedestrian bridges &
walkways
54
-
Live Load Reduction

The design live load determined using Table 205-1 of
the NSCP maybe reduced on any member supporting
more than 15 m2, except for floors in public assembly
and for live loads greater than 4.8 kPa:
R = r (A-15)
(1-1)
where:
R = reduction in percentage, %
A = area of floor or roof supported by the member, m2
r = rate of reduction equal to 0.08 for floors.
See NSCP Table 205-3 for roofs
55
Live Load Reduction (Cont.)


The reduction shall not exceed 40% for members
receiving load from one level only, 60% for other
members.
R can also be computed as
R = 23.1 (1 + D/L)
where:
D = dead load supported by the member, kPa
L = live load supported by the member, kPa
56
(1-2)
Live Load Reduction (Cont.)
As an alternate to Eq’n (1-1), the unit live load set in
NSCP Table 205-1 may be reduced on any member
having an influence area of 40 m2 or more using the
following:
𝐿 = 𝐿𝑜 0.25 + 4.57
where:
1
(1-3)
𝐴𝐼
AI = influence area, m2
L = reduced design live load/m2 of area supported by
member
Lo = unreduced design live load/m2 of area (Table 205-1)
57
Roof Live Load
Live loads on the roof caused by planters, people, or
by workers, equipment, and materials during
maintenance.
58
Roof Live Load
Ordinary flat, pitched, and curved roofs shall be
designed for the live loads specified in Table
205-3A or Table 205-3B of the 2015 NSCP.
www.ppfl.org
Flat Roof
59
www.staffordplastics.co.uk
Pitched Roof
archinspire.org
Curved Roof
Table 205-3A. Minimum Roof Live Loads
(NSCP, 2015)
ROOF SLOPE
METHOD 1
Tributary Area (m2)
0 - 20
20-60
> 60
Uniform load (KPa)
1. 33.3% slope. Arch and dome with
rise less than one-eighth of span.
1.00
0.75
0.60
2. 33% to less than 100% slope. Arch
and dome with rise one-eighth of
span to less than three-eights of
span.
0.75
0.70
0.60
3. 100% slope and greater. Arch and
dome with rise three-eights of span
or greater.
0.60
0.60
0.60
60
Table 205-3A (Cont.)
METHOD 1
Tributary Area (m2)
0 - 20
20-60
> 60
Uniform load (KPa)
ROOF SLOPE
4.Awnings except cloth covered.
5. Greenhouses, lath
agricultural buildings.
61
houses
and
0.25
0.25
0.25
0.50
0.50
0.50
Example 1.2*
The floor of the office
building shown is made of
100 mm thick lightweight
concrete. If the office floor
is a slab having a length of
6.0 m and width of 4.5 m,
determine the resultant
force caused by the dead
load and the live load.
62
*Problem 1-2, Hibbler. R. C., Structural Analysis, 8th Ed., p. 27
Wind Load

In the form of pressure or
suction on the exterior
surface
of
building
structures.

Generally, act perpendicular
to surfaces.
64
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Wind Load (Cont.)
Design wind loads for buildings and other
structures can be based on:
a) analytical procedure
• Directional procedure
• Envelope procedure
b) wind tunnel procedure
65
NSCP 2015
Wind-Tunnel Procedure

Consists of developing a small-scale model of
the building or structure

Involves testing the model in a wind tunnel to
determine the expected wind pressures etc.

Is expensive and may be utilized for difficult or
special situations.
66
Analytical Procedure

Typically used in most design offices.

It is fairly systematic but somewhat complicated to
account for the various situations that can occur.

The effect of wind on a structure depends on:
 Density of air
 Velocity of air
 Angle of incidence of wind
 Shape and stiffness of the structure
 Roughness of structure surface
67
Analytical Procedure
(2015 NSCP Section 207A)
Steps to Determine Wind Force on Main Wind
Force Resisting System (MWFRS)
Step 1: Determine risk category of building or
other structure, see Table 103-1
Step 2: Determine basic wind speed, V for the
applicable risk category (Figure 207A.51A, B or C)
68
Steps to Determine Wind Force on Main
Wind Force Resisting System (MWFRS)
Step 3: Determine wind load parameters:






69
Wind directionality factor, Kd (Section 207A.6)
Exposure category (Section 207A.7)
Topographic factor, Kzt (Section 207A.8)
Gust effect factor (Section 207A.9)
Enclosure classification (Section 207A.10)
Internal pressure coefficient, GCpi (Section 207A-11)
Steps to Determine Wind Force on Main
Wind Force Resisting System (MWFRS)
Step 4: Determine velocity pressure exposure
coefficient Kz or Kh (Table 207B.3.-1)
Step 5: Determine velocity pressure qz or qh
Step 6: Determine external pressure coefficient Cp
or CN (Figure 207B.4-1 to 4-7)
Step 7: Calculate wind pressure p on each building
surface
70
Step 1: Determine Risk Category
(see Table 103-1, NSCP, 2015)
Occupancy
Category
Occupancy or Functions of Structure
Essential Occupancies having surgery and emergency
Facilities treatment areas
Fire and police stations
Garages and shelters for emergency vehicles
and emergency aircraft
Structures and shelters in emergency
preparedness centers
Aviation control towers
Structures and equipment in communication
centers and other facilities required for
emergency response
I.
71
Table 103-1, NSCP, 2015 (Cont.)
Occupancy
Category
Occupancy or Functions of Structure
Essential Standby power-generating equipment for
Facilities Category I facilities
Tanks and other structures containing
housing or supporting water of other firesuppression material or equipment required
for the protection of Category I, II or III
structures
Public school buildings
Hospitals
Designated evacuation centers
I.
72
Table 103-1, NSCP, 2015 (Cont.)
Occupancy Occupancy or Functions of Structure
Category
II. Hazardous Occupancies and structures therein housing
or supporting toxic or explosive chemical
Facilities
or substances,
Non-building
structures
housing,
supporting, or containing quantities of toxic
or explosive substances
73
Table 103-1, NSCP, 2015 (Cont.)
Occupancy
Category
Occupancy or Functions of Structure
III. Special
Occupancy
Structures
Buildings with an assembly room having an
occupant capacity of 1000 or more,
Educational buildings with a capacity of 300
or more students,
Buildings used for college or adult
education with a capacity of 500 or more
students,
Institutional buildings with 50 or more
incapacitated patients, but not included in
Category I
74
Table 103-1, NSCP, 2015 (Cont.)
Occupancy
Category
Occupancy or Functions of Structure
Mental hospitals, sanitarium, jails, prison, and
III. Special
Occupancy other buildings where personal liberties of
Structures inmates are similarly restrained
All structures with an occupancy of 5000 or
more persons,
Churches, mosques, and other religious
facilities
75
Table 103-1, NSCP, 2015 (Cont.)
Occupancy
Category
Occupancy or Functions of Structure
Structures and equipment in power
III. Special
Occupancy generating stations, and other public utility
Structures facilities not included in Category I or
Category II above and required for
continued operation
76
Table 103-1, NSCP, 2015 (Cont.)
Occupancy
Category
Occupancy or Functions of
Structure
IV. Standard
Occupancy
Structures
V. Miscellaneous
Structures
All structures housing occupancies or
having functions not listed in Category I, II,
III and V
Private garages, carports, sheds, and fences
over 1.8 meters high
77
Step 2: Determine Basic Wind Speed, V
V = basic wind speed (km/hr), from Figure
207A.5-1A, B or C
= Corresponds to a 3-second gust speed
at 10m above ground
78
Basic Wind Speed, V
Figure 207A.5-1A
Basic Wind Speeds for
Occupancy Category
III, IV and V Buildings
and Other Structures
79
Basic Wind Speed, V (Cont.)
Figure 207A.5-1B
Basic Wind Speeds for
Occupancy Category II
Buildings and Other
Structures
80
Basic Wind Speed, V (Cont.)
Figure 207A.5-1C
Basic Wind Speeds for
Occupancy Category I
Buildings and Other
Structures
81
Step 3A: Wind Directionality Factor, Kd
Kd = obtained from Table
207A.6-1, NSCP 2015
= A factor that accounts
for the direction of wind
= used only when the
structure is subjected to
combinations of loads
(See Section 203.3 and
203.4, NSCP)
= 1.0 for wind acting alone
82
Step 3B: Exposure Category
Surface Roughness Categories (Section 207A.7.2)
Surface
Roughness
B
C
D
83
Definition
Urban and suburban areas, wooded areas, or other
terrain with numerous closely spaced obstructions
having the size of single-family dwellings or larger
Open terrain with scattered obstructions having
heights generally less than 9m. This category
includes flat open country, grasslands, and all water
surfaces in regions with records of extreme
typhoons
Flat, unobstructed areas and water surfaces. This
category includes smooth mud flats and salt flats
Step 3B: Exposure Category
Exposure Categories (Section 207A.7.3)
Exposure
Category
Definition
For buildings with a mean roof height of less than
or equal to 9m, Exposure B shall apply where the
ground surface roughness, as defined by Surface
Roughness B, prevails in the upwind direction for a
distance greater than 450m.
B
84
For buildings with a mean roof height greater than
9m, Exposure B shall apply where Surface
roughness B prevails in the upwind direction for a
distance greater than 790m or 20 times the height
of the building, whichever is greater.
Step 3B: Exposure Category
85
Figure C207A.7-3 Exposure B with Upwind Open Patches
Exposure Categories (Section 207A.7.3)
Exposure
Category
C
86
Definition
Exposure C shall apply for all cases where
Exposures B or D do not apply
Exposure Categories (Section 207A.7.3)
Exposure
Category
Definition
Exposure D shall apply where the ground surface
roughness, as defined by Surface Roughness D,
prevails in the upwind direction for a distance
greater than 1500m or 20 times the height of the
building, whichever is greater.
D
87
Exposure D shall apply where the ground surface
roughness immediately upwind of the site is
Exposure B or C, the site is within a distance of
180m or 20 times the height of the building,
whichever is greater, from an Exposure D
condition as defined in the previous sentence.
Step 3C: Topographic Factor, KZT
Kzt = obtained from Figure 207A.8-1, NSCP 2015
= A factor that accounts for wind speed increases
due to hills or escarpments
= 1.0 for flat ground
88
Step 3D: Gust Effect Factor, G
G = from Section 207A.9, NSCP, 2015
= 0.85 for rigid buildings (i.e. one-story bldgs.)
= for flexible buildings, see Section 207A.9.5
89
Step 3E: Enclosure Classification
(Section 207A.10)
All buildings shall be classified as enclosed,
partially enclosed, or open as defined in Section
207A.2
• Open building – a building having each wall at least
80% open.This condition is expressed for each wall by:
𝐴𝑜 ≥ 𝐴𝑔
(1-4)
where: 𝐴𝑜 = total area of openings in a wall that
receives positive external pressure (m2)
𝐴𝑔 = gross area of wall in which Ao is
2)
identified
(m
90
Step 3E: Enclosure Classification
(Section 207A.10)
• Partially enclosed building – a building that
complies with both of the following conditions:
1) The total area of openings in a wall that
receives positive external pressure exceeds the
sum of the areas of openings in the balance of
the building envelope (wall and roof) by more
than 10%.
2) The total area of openings in a wall that
receives positive external pressure exceeds
0.37 m2.
91
Step 3E: Enclosure Classification
(Section 207A.10)
• Enclosed building – a building that does not
comply with the requirements for open or
partially enclosed building
92
Step 3F: Internal Pressure Coefficient, GCpi
GCpi = depends upon the type of openings in the building
= signs indicate that either positive or negative
(suction) pressure can occur within the building
Table 207A.11 Internal Pressure Coefficient, NSCP, 2015
Enclosure Classification
Open Buildings
Partially Enclosed Buildings
Enclosed Buildings
93
GCpi
0
+0.55
-0.55
+0.18
-0.18
Step 4: Velocity Pressure Coefficient, Kz or Kh
Kz or Kh = obtained from Table 207B.3-1, NSCP 2015
= a function of height and depends on the
ground terrain or surface roughness
94
Step 4: Velocity Pressure Coefficient, Kz or Kh
95
Step 5: Velocity pressure qz
The velocity pressure (qz) in N/m2 at any height z,
qz = 0.613 Kz Kzt Kd V2
(1-5)
where:
V = basic wind speed (m/s) (Figure 207A.5-1A, B or C)
Kz = velocity pressure exposure coefficient (Table
207B.3-1)
Kzt = topographic factor (Figure 207A.8-1)
Kd = wind directionality factor (Table 207A.6-1)
96
Step 6: Wall or Roof Pressure Coefficient, Cp
Cp = See Fig.
207B.4-1,
207B.4-2,
207B.4-3,
NSCP 2015
97
Step 6: Wall or Roof Pressure Coefficient, Cp
98
Figure 207B.4-1, NSCP 2015
Step 7: Design Wind Pressure, p

Once the value of qz is obtained, the design
wind pressure, p can be determined from a list
of relevant equations (see Section 207B.4,
NSCP, 2015)

The choice depends on:
 Flexibility and height of structure
 Design for main wind-resisting
building’s components, or cladding
99
system,
Step 7: Design Wind Pressure, p (Cont.)
Design Wind Pressure for Enclosed and Partially
Enclosed Rigid Buildings
𝑝 = 𝑞𝐺𝐶𝑝 − 𝑞𝑖 𝐺𝐶𝑝𝑖
(N/m2)
where:
q = qz for the windward
wall at height z
above the ground
(Eq’n. 1-5)
= qh for the leeward walls, sidewalls, and roof at
height h (mean height of roof)
100
(1-6)
Step 7: Design Wind Pressure, p (Cont.)
qi = qh for windward walls, side walls, leeward
walls, and roofs of enclosed buildings and for
negative internal pressure evaluation in partially
enclosed buildings
qi = qz for positive internal pressure evaluation in
partially enclosed buildings where height z is
defined as the highest level of opening in the
building that could affect the positive internal
pressure.
101
Example 1.3*
The
enclosed
building
shown is used for storage
purposes and is located in
the Light Industrial Park in
Canlubang, Laguna on open
flat terrain. When the wind
is directed as shown,
determine the design wind
pressure acting on the roof
and sides of the building
based on NSCP provisions.
102
*Revised Problem 1.3, Hibbler. R. C., Structural Analysis, 8th Ed., p. 20
Laguna Maps
103
Earthquake Load

Inertial forces that act on a structure
due to earthquake induced ground
motion

Generally, act horizontally on each
element of the structure and are
proportional to their mass.

Thus, heavier structures are more
susceptible to earthquake loads.
www. finehomebuilding.com

Computation of earthquake loads is
the subject of Earthquake Engineering
104
Impact Load
➢ Dynamic
effect of a suddenly applied load, i.e. due to
moving vehicles, weight of elevator machinery
➢ Percentage
increase of the live load due to impact is
called the impact factor, I
105
1.7 Structural Idealization
Replacing an actual structure with a simple system
conducive to analysis
106
Structural Idealization (Cont.)
107
Tributary Area (Beams)

When flat surfaces such as walls, floors, or roofs
are supported by a structural frame, it is
necessary to determine how the load on these
surfaces are transmitted to the supporting
elements.

The loads transferred from the slab to the
supporting beams depend on the geometry of
the slab.
108
One-Way Slab
If the ratio of width S to
length L,
S
 0.50
L
• most of the load is carried in
the short direction to the
supporting beams
• one-way action is obtained
even though supports are
provided on all sides
109
Two-Way Slab
If the ratio of width S to
length L,
S
 0.50
L
The slab is classified as twoway slab.
110
Equivalent Slab Load Transferred to
Supporting Beams (One-Way Slab)
One-Way Slab
Beam along long span
Wu
B
D
C
L
Tributary
Width
A
D
W (kN/m) = W (kPa) x Tributary Width
Beam along short span
C
No load
S
111
A
C
Equivalent Slab Load Transferred to
Supporting Beams (Two-Way Slab)
Two-Way Slab
Beam along long span
B
Wu
D
L
S/2
A
45°
S
112
C
D
C
L-S
S/2
w (kN/m) = w (kPa) x S/2
Equivalent Slab Load Transferred to
Supporting Beams (Two-Way Slab)
Two-Way Slab
Beam along short span
B
D
Wu
L
C
A
S
A
45°
S
113
C
w (kN/m) = w (kPa) x S/2
Tributary Area (Columns)
Tributary Area
for Column A1
Tributary Area
for Column C2
Extends from the
member in question
halfway
to
the
adjacent members
in each direction
Tributary Area
for Column F4
114
Example 1.4
A reinforced concrete building floor system is to
be designed for the following service loads:
Dead Load:
Self-weight
Topping and finishes
Utilities
Partition loads
-
23.544 KN/m3
1.10 KPa
0.50 KPa
1.00 KPa
Live Load (Office)
-
2.40 KPa
115
The floor system
consists of a
A
continuous slab
built
monolithically
with its supporting
beams, as shown in
plan in the figure.
7.00m 4.25m 4.375m
Example 1.4 (Cont.)
3.375m 4@3.25 = 13.0m 3.375m
Assume all the beams
to have width of 0.25 m
116
Floor Plan
Section A-A
A
117
B-1
S1
C2
B-2
S2
B-3
S3
B-4
3.375m 4@3.25 = 13.0m 3.375m
Floor Plan
7.00m 4.25m 4.375m
G-3
a) beams B-1 to B-4
(kN/m)
b) girders G-1 to G-3
(kN/m)
c) columns C1, C2 (kN)
C1
G-2
If the floor slab has a
thickness of 100 mm,
determine the total dead
load and live load
transferred from the slab
to
the
following
supporting members:
G-1
Example 1.4 (Cont.)
References
NSCP 2015 National Structural Code of the Philippines
Hibbler, R. C. 2012. Structural Analysis. 8th Edition.
Prentice Hall: New Jersey.
Kassimali, A. 2010. Structural Analysis. 4th Edition.
PSW Kent: Boston.
Oreta, Andres Winston C. 2011. Introduction to
Structural Analysis.
www.slideshare.net/andyoreta/introduction-on-theory-ofstructures
118
Thank you for
listening!
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