1-introduction to structural analysis (2014)

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CE3155 Structural Analysis

Introduction to Structuralna yss

Professor Tan Kiang Hwee

Dept of Civi l & Environmental Engineering

Structural Analysis

- to predict the performance of a given structure under

prescr e oa s an or o er ex erna e ec s, suc assupport movements and temperature changes.

Performance characteristics

- , . ., ,

forces & bending moments

- , . ., ,

- support reactions

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Structural Elements

• Tie rods• subjected to tensile

force only

• rather slender

• made of rods, bars,

angles or channels

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•

• usually straight

horizontal members used

o carry ver ca oa s

• primarily design to resist

bendin moment & shear Simply-supported

(s.s.) beamCantilever beam

• steel beams usuallyhave flanged sections

• concre e eams ave

rect. or T-cross sections

with reinforcing barss.s. beam withcantilever end

Continuous beam

Steel flan ed Reinforced concrete

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section T-section


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• Columns

• general vertical and resist

compressive loads

• steel columns usually in the formof tubes and wide-flan e cross-

section

• concrete columns are of circular

. -

reinforcing bars

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Structural Systems

- Combination of

structural elements andthe materials from

• Trusses• Frames

which they are

composed of • Cables & Arches

•- Four basic types

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• Trusses

• consist of pin-jointed slender elements, usually arranged in

triangular fashion•

• planar truss – used for bridge & roof support

• space truss – used for derricks and towers

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• rames

• composed of beams and

columns that are either pin or fixed

connecte

• members subject to axial, shear

& moment loadings

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• usually flexible & carry their

loads in tension

• Arches

• achieve its strength in

• commonly used to support

bridges and building roofs • must be rigid; results in

secondary loadings involving

• used in bridge structures,

dome roofs, etc.

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• Surface Structures

• made using a very thin material compared to other dimensions; material

ac s as a mem rane su ec e o pure ens on; or

• made of rigid material (e.g. reinforced concrete) shaped as folded plates,

cylinders, etc. (known as thin plates & shells), supporting loads primarily in

ens on or compress on

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Su ort Connections

• Pin connection

• Roller su ort

• Fixed joint

“roller-supported’ “fixed-supported”“pin-supported”

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#unknowns = 1

#unknowns = 1

=

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#unknowns = 1

#unknowns = 2

#unknowns = 2

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#unknowns = 3

Idealized structure

Idealized beam

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4.8 kN/m2

0.75 m

0.75 m

1.5 m

1.5 m

3 m0.75 m

0.75 m

4.8 x 1.5 = 7.2 kN/m

Idealized framing plan

3 m

5.4 kN 5.4 kN10.8 kN

. m. m10.8 kN 7.2 x 3/2 =10.8 kN

Idealized beam CD Idealized girder AE

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The flat roof of thesteel-frame buildingshown on the rightsuppor s a o a oaof 2 kN/m2.

3 m

Determine the roofload within ABCD

that is transmitted tobeam BC .

1 . 5 = 3 k N /

2 x

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1.5 m 1.5 m

16


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4 Governing conditions ofstructural behaviour

1. Equil ibr ium

relations among forces F i (or stresses) F 2

2. Compatibil ity (or kinematics)

relations among displacements ∆i (or

F 1

s ra ns

3. Constitutive relations

Force-Displacement relations (or

Stress-Strain relations F i

If only the equilibrium equations are needed to solve for F i , then thestructure is statically determinate.

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• Determinac

• structures with more unknown

forces than available equilibrium

indeterminate

• for a coplanar (2D) structure, there

are 3 equil. eqs. for part/whole of

structure being considered:

considered, and r the number of

force and moment reaction

• Degree of indeterminacy = (r – 3n)

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Examples - Beams

= 3,n = 1, 3 = 3(1) sta t ic a lly de term ina te

r = 5,n = 1, 5 > 3(1)sta t ic a lly inde term ina te

to 2 nd deg ree

r = 6, n = 2, 6 = 3(2)

r = 10, n = 3, 10 > 3(3)sta t ic a lly de term ina te

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to 1 s deg r ee

Examples - Frames

= 9, n = 1, 9 > 3(1)sta t ic a lly inde term ina te

to the 6 th deg ree

= 9, n = 2, 9 > 3(2)sta t ic a lly inde te rm ina te

to the 3 rd deg ree

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• Stabilit• members of a structure must be properly held or constrained by

their supports

A coplanar structure is unstable if it is:

• partially constrained (r < 3n); or

• improperly constrained (r 3n)

- Support reactions are concurrent or

parallel

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r = 3, n = 1, 3 = 3(1)sta t ic a lly de term ina te r = 3 n = 1 3 = 3 1 = =Rea c t io ns a re no t

concu r ren t /pa ra l l e l

stable

sta t ic a lly de termina te

Rea c t ions c onc urren t

unstable

, ,

unstable

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Test Your Understanding –Introduction to Structural Analysis1. What are the basic structural elements and what are the rimaril

subjected to?

Ans:

2. What are the four basic types of structural systems?

Ans:.

.

Ans:

4. A structurre is staticall determinate if the number of unknown forces is lessthan the number of equilibrium equations. True o r Fa lse ?

Ans:.

5. I a structure s unstable, t does not matter whether t s stat cally determnateor not. True o r Fa lse ?

Ans

©Tan K H, NUS 23

Hibbeler, R.C., Structural Analysis , 8 Edition in SI units,

Chapters 1 & 2.

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1-introduction to structural analysis (2014)

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