CEU3 SA LN1 Introduction

Structural Analysis I MOM Mony, PhD

Adjunct Professor of Civil Engineering

Norton University

Phnom Penh, Cambodia

Academic Year 2013-2014

Lecture 1: Introduction

Historical development of

structural systems

Classification of structures

Idealization of structures

Design process: from

analysis to design

2

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)

3


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.

4


Structural Systems

5

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.


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.



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.



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.



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.

Classification of Structures

10

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

11

Tension Structures

12

Compression Structures

13

Truss

Loads applied

only on the

joints

Members of a

truss are either

tension or

compression

14

Shear Structures

Shear Wall Behavior Frame Behavior

15

Bending Structures

16

Surface Structures

17

Shell

Structure

Membrane

Structure

Surface

Structure

Idealization of Structures

18

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

19

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

+

20

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 -

Physical 21

22

23

24

25

Loads on Structures

26

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

27

Design Loads on Building

Structures

28

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

29

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

30

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

31

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

32

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

33

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

34

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%

35

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

36

Wind Load (cont..)

Design wind pressure

p =qzGCp (3)

p: design wind pressure, G: gust factor,

Cp: external pressure coefficient

37

Basic Wind Speed (V)

38

Wind Directionality Factor (Kd)

The factor shall be

determined (Table 6-6). It

shall only be applied when

used in load combination.

39

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

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).

40

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

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.

41

42

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

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

44

Case 1: low-rise buildings, and component & cladding

Case 2: all buildings except those in low-rise buildings

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

45

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

46

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

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.

47

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

48

49

Buildings

50

Gable/Hip Roof

51

Monoslope Roof

52

Mansard Roof

53

Earthquake Load

Base shear

54

V = CsW

V: base shear

Cs: seismic

response

coefficient

W: dead load

of building

Sds: design spectral acceleration in

the short period range

R: response modification factor

(1.25-8)

I: importance factor

55

Cs= Sds/(R/I)

Hydrostatic and Soil Pressure

Hydrostatic/Soil Pressure

p: pressure

𝛾: unit weight of liquid/soil

h: height below the surface

56

Loads on Bridges

57

Highway Bridges 58

1k = 4.45 kN

1 ft = 0.305 m

Railroad Bridges

59

Impact Factor

60

Design Loads

61

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)

62

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)

63

Load Transfer

64

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

65

Load Transfer Path is difficult to

Determine

Transfer of a Point Load to Point Supports Through Various Mediums

Point Line Area Volume

66

Simplified Load Transfer

Transfer of Area Load

To Lines To Points To Lines and Points

67

Simplified Load Transfer

Transfer of Area Load

To Lines To Points

68

Two-way slab-beams

Square slab

69

Two-way slab-beams

Rectangular slab

70

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

71

Design Process: from analysis

to design

72

73

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

74

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

75

76

Thank You !

Q & A

77

Documents

CEU3 SA LN1 Introduction