ceu3 sa ln1 introduction
TRANSCRIPT
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Structural Analysis I MOM Mony, PhD
Adjunct Professor of Civil Engineering
Norton University
Phnom Penh, Cambodia
Academic Year 2013-2014
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Lecture 1: Introduction
Historical development of
structural systems
Classification of structures
Idealization of structures
Design process: from
analysis to design
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Historical Development of
Structural Systems
Middle of 17th century
Trial and error and rule of thumb
Pyramid, Egypt (3000 B.C.)
Greek temples (500-200 B.C.)
Roman Coliseums and Aqueducts
(200 B.C.-A.D. 200)
Gothic Cathedrals (A.D. 1000-1500)
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Historical Development of
Structural Systems
Fathers of the Theory of Structures
Galileo Galilei (1564-1642), Italian. He
analyzed the failure of simple structures
and predicted the strengths of beams.
Robert Hooke (1635-1703), English. He
developed the law of linear relationships
between force and deformation of
materials.
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Historical Development of
Structural Systems
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Sir Isaac Newton (1642-1727), English.
He developed the law of motion
and calculus.
Johann Bernoulli (1667-1748), Swiss.
He developed the principle of virtual
work.
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Historical Development of
Structural Systems 6
Leonhard Euler (1707-1783), Swiss. He developed the theory of buckling of columns.
Charles-Augustin de Coulomb (1736-1806), French. He developed the analysis of bending of elastic beams.
Claude-Louis Navier (1785-1836), French. He studied on the elastic behavior of structures.
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Historical Development of
Structural Systems 7
Benoit Paul Emile Clapeyron (1799-1864), French. He developed the three-moment equation for the analysis of continuous beams.
James Clerk Maxwell (1831-1879), Scottish/English. He developed the method of consistent deformation (Force Method), and the law of reciprocal deflections.
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Historical Development of
Structural Systems 8
Christian Otto Mohr (1835-1918), German. He developed conjugate-beam method for calculating deflection of beams, and Mohr’s circle for stress and strain.
Carlo Alberto Castigliano (1847-1884), Italian. He developed the theory of least work.
Charles E.Greene (1842-1903), . He developed the moment-area method.
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Historical Development of
Structural Systems 9
Heinrich Mueller-Breslau (1851-1925), German. He developed the principle of influence line.
George A. Maney (1888-1947),American. He developed the slope-deflection method.
Hardy Cross (1885-1959), American. He developed the moment-distribution method in 1924.
Computer-oriented methods of structural analysis are contributed by John Hadji Argyris (Geek), RayWilliam Clough (American, 1920), S. Kelsey, R.K.Livesley, H.C.Martin, M.T.turner,E.L Wilson, Olgierd Cecil Zienkiewicz (1921-2009), Polish-British.
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Classification of Structures
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Types of Structures
Buildings (reinforced concrete, steel, composite frames)
Bridges (beam/girder, suspended, truss)
Shell structures (e.g. dome,..)
Membrane structures
Hydraulic structure (e.g. dams,…)
Offshore structures (e.g. petroleum platform,…)
Nuclear reactors
Ships, vessels,
others
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Tension Structures
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Compression Structures
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Truss
Loads applied
only on the
joints
Members of a
truss are either
tension or
compression
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Shear Structures
Shear Wall Behavior Frame Behavior
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Bending Structures
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Surface Structures
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Shell
Structure
Membrane
Structure
Surface
Structure
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Idealization of Structures
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Idealized Structures
Simplified representation of real
structures for the purpose of
analysis.
Plane (2D) vs Space (3D) structures
3D structures can be simplified by
sub-dividing into 2D structures
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Converting Structure to 2D Model
L1
P
P
P
L2
L2
L1
P
Structure 2D Frame
(a) Building Frames
Structure 2D Truss/Frame
(b) Trusses and Industrial Bents
Deck Slab-Structure 2D Frame
(c) Bridge Deck
Grid-Plate
Arch or Barrel 2D-Frame
Fig. 2 Symmetrical/ Regular Structure with symmetrical loads
+
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Beams, Columns, Two-way Slabs, Flat Slabs, Pile caps
Shear Walls, Deep Beams, Isolated Footings, Combined Footings
Sub-structure and Member Design
Frame and Shear Walls Lateral Load Resisting System
Floor Slab System Gravity Load Resisting System
Building Structure
Floor Diaphragm
The Building Structural System -
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Loads on Structures
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Loads on Structures
Dead loads
Live loads
Impact
Wind loads
Snow loads
Earthquake loads
Hydrostatic and soil pressures
Thermal and other effects
Tributary areas of loads transmitting to structural systems
Design loads by ASCE 07-11
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Design Loads on Building
Structures
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Dead Loads
Materials Steel 77 kN/m3
Aluminum 25.9 kN/m3
Reinforced concrete (normal weight)
23.6 kN/m3
Reinforced concrete (light weight)
(14.1-18.9) kN/m3
Brick 18.9 kN/m3
Wood (5.3-5.8) kN/m3
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Dead Loads (cont..)
Building Component Weight
Ceiling
Gypsum or suspended metal lath 0.48 kN/m2
Acoustical fiber tile or channel ceiling
0.24 kN/m2
Roof
Three-ply felt tar and gravel 0.26 kN/m2
2-in. (50 mm) insulation 0.14 kN/m2
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Dead Loads (cont.)
Walls and Partitions
Gypsum board (1 in. (25mm) thick)
0.19 kN/m2
Brick (per inch thickness) 0.48 kN/m2
Hollow concrete block (12 in. thick)
Heavy aggregate 2.83 kN/m2
Light aggregate 2.63 kN/m2
Clay tile (6 in. thick) 1.44 kN/m2
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Live Loads
Assembly areas and theaters
Fixed seats (fastened to floor) 2.87kN/m2
Lobbies 4.79 kN/m2
Stage floors 7.18 kN/m2
Libraries
Reading rooms 2.87 kN/m2
Stack rooms 7.18 kN/m2
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Live Loads (cont..)
Office Buildings
Lobbies 4.79 kN/m2
Offices 2.40 kN/m2
Residential
Habitable attics and sleeping areas 1.44 kN/m2
Uninhabitable attics with storage 0.96 kN/m2
All other areas 1.92 kN/m2
Schools
Classrooms 1.92 kN/m2
Corridors above the first floor 3.83 kN/m2
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Live Load Reduction
When influence areas (KA) ≥ 37.2 m2 L =Lo (0.25 + 4.57/√KA
where Lo: Live Load(original)
L: reduced value of live load,
A: tributary area (m2),
K: live load element factor (4 for columns, 2 for beams)
But L ≥ 50% of Lo for column or beam supporting a single floor; L ≥ 40% of Lo for column or beam supporting two or more floors
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Live Load Impact Factor
(Increase in %)
Loading Case -Supports of elevators and elevator machinery 100%
-Supports of light machinery, shaft, or motor driven 20%
-Supports of reciprocating machinery or power-driven units 50%
-Hangers supporting floors or balconies 33%
-Cab-operated traveling crane support girders and their connections25%
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Wind Load
Static wind pressure (qs)
qs =0.613V2 (1) where V: basic wind speed (m/s)
Velocity wind pressure at height z above ground level (qz)
qz = qsI KzKztKd (2)
I: importance factor, Kz: velocity exposure coefficient,
Kzt: topographic factor, Kd: wind direction factor
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Wind Load (cont..)
Design wind pressure
p =qzGCp (3)
p: design wind pressure, G: gust factor,
Cp: external pressure coefficient
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Basic Wind Speed (V)
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Wind Directionality Factor (Kd)
The factor shall be
determined (Table 6-6). It
shall only be applied when
used in load combination.
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Structure Type Kd
Building 0.85
Arched roof 0.85
Chimneys, tanks, and similar structures: -square
-round & hexagonal
0.90
0.95
Signs, lattice framework 0.85
Trussed towers -triangular, square, rectangular
-other cross sections
0.85
0.90
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Important Factor (I) Buildings are classified as four
categories depend on the hazard to human life in the event of failure. The factor is used to adjust wind speed associated with annual probability of 0.02 (50-year MRI) to other probabilities (25-year, 100-year,…others MRI).
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Category Description I
Non-hurricane hurricane
I: low Agricultural, temporary, minor storage facilities 0.87 0.77
II Except those listed in I, III, and IV 1.00 1.00
III:
substantial
Facilities with>300 people congregate in one area; day-care facility
with capacity > 150 people; school with capacity > 250 people;
university with capacity >500 people; health care facility with
capacity > 50 people; jail and detention facilities; power generating
and public utility facilities; toxic, explosive, hazardous storage.
1.15 1.15
IV: essential Hospitals; fire, police stations; emergency facilities; communication
towers including aviation control towers; national defense facilities.
1.15 1.15
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Velocity Pressure Exposure
Coefficient (Kz)
The coefficient depends on the exposure categories and its height above ground (Table 6-5):
Exposure A. large city center with at least 50% of building having a height > 70 ft (21.3 m).
Exposure B. urban and suburban areas, wooden area, or other terrain with numerous obstructions having the size of single family dwelling or larger. The terrain that is in the upwind direction with a distance at least 1,500 ft (460 m) or 10 times of the height of the building, whichever is greater.
Exposure C. open terrain.
Exposure D. wind flowing from open water for a distance at least 1 mile (1.61 km); extending inland from the shoreline a distance of 1,500 ft (460 m) or 10 times of the height of the building, whichever is greater.
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43 Height (z) Exposure
ft m A B C D
Case 1 Case 2 Case 1 Case 2 Cases
1&2
Cases
1&2
0-15 0-4.6 0.68 0.32 0.70 0.57 0.85 1.03
20 6.1 0.68 0.36 0.70 0.62 0.90 1.08
25 7.6 0.68 0.39 0.70 0.66 0.94 1.12
30 9.1 0.68 0.42 0.70 0.70 0.98 1.16
40 12.2 0.68 0.47 0.76 0.76 1.04 1.22
50 15.2 0.68 0.52 0.81 0.81 1.09 1.27
60 18.0 0.68 0.55 0.85 0.85 1.13 1.31
70 21.3 0.68 0.59 0.89 0.89 1.17 1.34
80 24.4 0.68 0.62 0.93 0.93 1.21 1.38
90 27.4 0.68 0.65 0.96 0.96 1.24 1.40
100 30.5 0.68 0.68 0.99 0.99 1.26 1.43
120 36.6 0.73 0.73 1.04 1.04 1.31 1.48
140 42.7 0.78 0.78 1.09 1.09 1.36 1.52
160 48.8 0.82 0.82 1.13 1.13 1.39 1.55
180 54.9 0.86 0.86 1.17 1.17 1.43 1.58
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Height (z) Exposure
ft m A B C D
Case 1 Case 2 Case 1 Case 2 Cases
1&2
Cases
1&2
200 61.0 0.90 0.90 1.20 1.20 1.46 1.61
250 76.2 0.98 0.98 1.28 1.28 1.53 1.68
300 91.4 1.05 1.05 1.35 1.35 1.59 1.73
350 106.7 1.12 1.12 1.41 1.41 1.64 1.78
400 121.9 1.18 1.18 1.47 1.47 1.69 1.82
450 137.2 1.24 1.24 1.52 1.52 1.73 1.86
500 152.4 1.29 1.29 1.56 1.56 1.77 1.89
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Case 1: low-rise buildings, and component & cladding
Case 2: all buildings except those in low-rise buildings
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Topographic Factor (Kzt)
Assumption
No significant terrain features exist over sufficiently large distance: radius of 2 miles (3.2 Km) or 100H,
The structure locates in the upper one-half of the height of hill or escarpment,
The height of the hill (H) > 15 ft (4.5 m) in exposure C & D, and 60 ft (18 m) in exposure B, and
H/Lh ≥ 0.2
Topographic factor (Kzt)
When V(z) =3-s gust speed at height z above ground in horizontal with no topographic feature. Kzt = [V(z,x)/V(z)]2
With topographic feature
Kzt = (1 + K1K2K3)2 , where K1 : account for the shape of
topographic feature K2 : account for the distance from the crest K3 : account for the height above the surface
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Topographic multipliers K1, K2, K3 (exposure C)
H/Lh K1
x/Lh K2
z/Lh K3
Ridge Escarp. Hill Escarp. Others Ridge Escarp. Hill
0.20 0.29 0.17 0.21 0.00 1.00 1.00 0.00 1.00 1.00 1.00
0.25 0.36 0.21 0.26 0.50 0.88 0.67 0.10 0.74 0.78 0.67
0.30 0.43 0.26 0.32 1.00 0.75 0.33 0.20 0.55 0.61 0.45
0.35 0.51 0.30 0.37 1.50 0.63 0.00 0.30 0.41 0.47 0.30
0.40 0.58 0.34 0.42 2.00 0.50 0.00 0.40 0.30 0.37 0.20
0.45 0.65 0.38 0.47 2.50 0.38 0.00 0.50 0.22 0.29 0.14
0.50 0.72 0.43 0.53 3.00 0.25 0.00 0.60 0.17 0.22 0.09
3.50 0.13 0.00 0.70 0.12 0.17 0.06
4.00 0.00 0.00 0.80 0.09 0.14 0.04
0.90 0.07 0.11 0.03
1.00 0.05 0.08 0.02
1.50 0.01 0.02 0.00
2.00 0.00 0.00 0.00
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H: height of hill or escarpment,
Lh: distance upwind of crest is ½ of H,
x: distance (upwind or downwind) from the
crest to the building site,
z: height above local ground level
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Design Wind Pressures or Loads
Gust Effect Factor (G)
For rigid building: natural frequency of vibration <1 Hz or ratio h/ least horizontal dimension < 4, G = 0.85.
For flexible building: natural frequency of vibration > 1Hz or ratio h/ least horizontal dimension > 4, Gf can be calculated by formula (ASCE 6.5.8.2).
Design Wind Pressure (p) or Loads (F)
Design procedure: simplified or analytical,
Enclosure classification: enclosed, partially enclosed or open (ASCE 6.2)
Building type: rigid or flexible; height of building,
Wind resisting systems: main wind force resisting system (MWFRS); components & cladding,
Sign convention: positive pressure acts toward the surface and negative pressure acts away from the surface.
Note: Wind Pressures (p) is applied when the structure is enclosed, partially enclosed or for the components and cladding. Wind loads (F) is applied for open structures.
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External Pressure Coefficient (Cp)
Wall Pressure Coefficient (Cp)
Surface L/B Cp
Windward wall All values 0.8
Leeward wall 0-1 -0.5
2 -0.3
>4 -0.2
Side wall All values -0.7
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Buildings
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Gable/Hip Roof
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Monoslope Roof
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Mansard Roof
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Earthquake Load
Base shear
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V = CsW
V: base shear
Cs: seismic
response
coefficient
W: dead load
of building
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Sds: design spectral acceleration in
the short period range
R: response modification factor
(1.25-8)
I: importance factor
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Cs= Sds/(R/I)
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Hydrostatic and Soil Pressure
Hydrostatic/Soil Pressure
p: pressure
𝛾: unit weight of liquid/soil
h: height below the surface
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Loads on Bridges
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Highway Bridges 58
1k = 4.45 kN
1 ft = 0.305 m
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Railroad Bridges
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Impact Factor
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Design Loads
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Factor Loads and Load Combination
(ASCE 7-11)
1.4D (1)
1.2D + 1.6L +0.5 (Lr, or S or R) (2)
1.2D+1.6(Lr or S or R)+(1.0L or 0.5W) (3)
1.2D+1.0W+1.0L+0.5(Lr or S or R) (4)
1.2D+1.0E+1.0L+0.2S (5)
Control Overturning or Sliding
0.9D+1.0W (6)
0.9D+1.0E (7)
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Factor Loads and Load Combination
(ASCE 7-11) (cont..)
If fluid load is present: 1.4F to be included in (1)
If earth pressure is present: 1.6H to be included in (2,6.7); if it is permanent present: 0.9H in (2,6,7)
If earthquake designed for service-level: 1.4E in (5)
If wind is designed for service-level: 1.6W in (4,6) and 0.8W in (3)
If small live loads: 0.5L in (3,4,5) except for garages, areas of public assembly, areas where live loads is greater than 100 psf (4.78 kN/m2)
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Load Transfer
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Tributary Areas of Load Transfer
How do the loads transfer in structures from roof to foundation?
In general assumption
Slabs to beams/girders
Beams/girders to columns
Columns to footings
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Load Transfer Path is difficult to
Determine
Transfer of a Point Load to Point Supports Through Various Mediums
Point Line Area Volume
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Simplified Load Transfer
Transfer of Area Load
To Lines To Points To Lines and Points
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Simplified Load Transfer
Transfer of Area Load
To Lines To Points
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Two-way slab-beams
Square slab
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Two-way slab-beams
Rectangular slab
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Lateral Loads on Buildings
WIND LOAD = W kg/sq.m
Line Load = W.B
1. Wind Loads
2. Effects of Seismic Loads
Assumed Loading Simplified Loading
B
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Design Process: from analysis
to design
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Design Process
Planning: functional requirements of the proposed structures
Preliminary design: estimate the member sizes of the proposed structures based on approximate analysis, past experiences, and code requirements
Loads estimate: consider all loads may act on the structures and how their load transfer
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Design Process
Structural Analysis: analyze the structures to determine the stresses or stress resultants in the members and deflections at various points of the structures
Safety and Serviceability Check: determine whether the structures satisfied the safety and serviceability of the design codes. If yes, design drawings and specifications are prepared and then construction begins. If not, revise the structural design
Revised Structural Design: either revise materials or member sizes of the structures
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Thank You !
Q & A
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