Introduction to ESA

7/23/2019 Introduction to ESA

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ELEMENTARY STRUCTURAL ANALYSIS

STRUCTURE:

A body capable of resisting applied loads without any appreciable deformations. The function of structure is to transmit loads

from one point to other point. A structure may be composed of various structural elements interconnected so as to form a stablebody and able to serve the purpose for which it is created.

STABLE AND UNSTABLE STRUCTURES:

A stable structure is one which does not change its shape and position upon application of loads where as an unstable structure

changes its shape and position.

STRUCTURAL ELEMENTS:Structural analysis techniques divide the structure into no of elements. Each element is relatively simple making the calculations

of properties of individual elements easy. Assembly of elements in accordance with geometry of element produces a model of

complete structure that can be used to investigate the effects of applied loading depending upon problem in hand. This

classification is used for the modeling of the elements to form a structure.

Structures are idealized using line, plate or brick elements.


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Line Elements:

Line elements are used to model structural elements that have one dimension dominant over the other two.

Typical examples are: Truss members, Beams, Columns etc.

Structures consisting of entirely line elements are called skeleton or frame structures.

Plate Elements:

Plate elements are used to model structural components such as slabs, shells of which two dimensions are dominant over the third

one. The structural action is usually two dimensional.


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Brick Elements:

Brick elements are used to model structures such as thick slabs, foundations where all the three dimensions are comparable.

ANALYSIS OF STRUCTURE:

It is a process of determining the internal forces generated within structure in response to the applied loads. These forces may be

axial forces, shear forces or bending moments.

Simultaneously we also determine various deformations produced in structure on load application.

In structural analysis internal forces are found in terms of diagrams i.e, Axial force diagram (AFD), Shear force diagram (SFD)

and Bending moment diagram (BMD).

The major type of internal stresses are:

1. Flexural stresses.

a. Compression.

b. Tension.

2. Axial stresses.

3. Shear stresses.

4. Torsional stresses.


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STRUCTURAL LOADING:

The loads which can be applied to a structure are of following types;

Types of loads:

1.

Gravity Loads

a. Dead Loads.

This dont change magnitude and location.

b. Live Loads.

This may change magnitude and location.

2. Lateral Loads

a. Wind loads (Dynamic in nature).

b. Earth quake loads (Dynamic in nature).

Forms of loads:

1. Point Load.

2. Uniformly distributed Load.

3. Uniformly varying Load.

4. Line Load.

TYPE OF SUPPORTS:

1. Roller support (One degree constraint).

2. Hinge support (Two degree constraint).

3. Fixed support (Three degree constraint).


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Structural LoadsStructural Loads

A load may be defined as a force tending to effect and produce

deformations, stresses or displacements in the structure.


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Dead loads.

Live loads.

Dynamic loads.

Wind loads.

Earthquake loads.

Snow loads.

Types of Loads in Structures


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Weight of the structure.

Floors, Beams, Roofs. Loads that are always there

Dead Loads


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Loads that may move or

change mass or weight: forexample: People, furniture,

equipment.

Minimum design loadings

are usually specified in thebuilding codes.

Live Loads


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Example of Live Load

Live Load = 100 N/mm^2Ballroom


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Moving loads (e.g. traffic)

Impact loads

Gusts of wind

Loads due to cycling machinery

Dynamic Loads


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Water, = density

h

P = gh

Load Example - water in a dam


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Structure loaded when base is shaken.

Response of structure is dependent on the

frequency of motion.

Earthquake Loads

Gravity Load

Lateral

LoadWind load

LateralLoad

Seismic

load

UniformlyincreasingLoad

Snow load


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Wind Loads

The amount of wind load is dependent on the

following:

Geographical location,

The height of structure,

Type of surrounding physical environment,

The shape of structure,

Size of the building.


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Snow Loads

The amount of snow load on a roof structure

is dependent on a variety of factors:

Roof geometry,

Size of the structure,

Insulation of the structure,

Wind frequency,

Snow duration,

Geographical location of the structure.


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Vertical: Gravity Lateral: Wind, Earthquake

Loads Acting in Structures


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Sliding Overturning

Global Stability


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100lb

Compression

100lb

Tension

Forces in Structural Elements


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100lb

Bending

Torsion

Forces in Structural Elements


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Arch

Typical Structural Systems


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C

T

CCT

Forces in Truss Members

Truss



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Frame



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Displacement

Force


Beam


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Tension

Compression

LoadsTypes of Structural Elements - Beams


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Force, P

2/3 P

Span, L

1/3 L 2/3 L

1/3 P

Force Transfer from Beams to Supports


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18,000 lb

8,000 lb 32,000 lb

22,000 lb

L = 60 ft

30 ft 30 ft

15 ft 45 ft

Force Transfer Example - Bridge


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Concentrated Load (Point Load)

P

Uniformly Distributed Load (UDL)

Uniformly Increasing Load

w

Area Load

wwL/2

L

1/3L1/3L1/3L

w

L

wL

5

Load Representation


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Indeterminate StructuresIndeterminate Structures

Architecture 4.440


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Forces in the Legs of a StoolForces in the Legs of a Stool


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ThreeThree--Legged StoolLegged Stool

Statically determinate

One solution for the axial forcein each leg

Why?

3 unknowns

3 equations of equilibrium

Uneven floor has no effect


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FourFour--Legged StoolLegged Stool

Statically indeterminate

A four legged table on an

uneven surface will rock

back and forth

Why?

It is hyperstatic:

4 unknowns

3 equations of equilibrium


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Infinite solutions exist

Depends on unknowable support

conditions

A four legged table on an uneven

surface will rock back and forth

The forces in each leg are constantly

changing

Fundamental difference between hyperstatic and static structures


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Forces in the Leg of a StoolForces in the Leg of a Stool

Statically

determinate

Statically

Indeterminate

(hyperstatic)


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ThreeThree--Legged StoolLegged Stool

Design for a personweighing 180 pounds

60 pounds/leg

Regardless of uneven

floor

180 lbs

60 lbs

60 lbs60 lbs


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Collapse of a ThreeCollapse of a Three--Legged StoolLegged Stool

Design for a personweighing 180 pounds

If the safety factor is 3:

Pcr = 3(60) = 180 lbs

And each leg would be

designed to fail at a load of180 pounds

The stool would carry a

total load of 540 pounds

540 lbs

180 lbs

180 lbs180 lbs


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Elastic Solution for 4Elastic Solution for 4--Legged StoolLegged Stool

180 lbs

45 lbs

45 lbs45 lbs

45 lbs

Design for a person

weighing 180 pounds

45 pounds/leg

But if one leg does nottouch the floor


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180 lbs

90 lbs

90 lbs

If one leg doesnt touch the

floor, the force in it is zero.

If one leg is zero, then the

opposite leg is also zero by

moment equilibrium.

The two remaining legs

carry all of the load:

90 pounds/leg


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Therefore

All four legs must bedesignedto carry the 90

pounds (since any two

legs could be loaded)

180 lbs

90 lbs

90 lbs


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If the elastic solution is

accepted, with a load in eachleg of 45 pounds, thenassuming a safety factor of 3

gives:

Pcr = 3(45 lbs) = 135 lbs

And each leg would bedesigned to fail at a load of135 pounds


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270 lbs

135 lbs

135 lbs

Now imagine the load is

increased to cause failure

When load is 270 lbs, thetwo legs will begin to fail

As they squash, the

other two legs will start to

carry load also


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Collapse of a 4Collapse of a 4--Legged StoolLegged Stool

540 lbs

135 lbs

135 lbs135 lbs

135 lbs

At final collapse state, all four legs

carry 135 pounds and the stool

carries 540 pounds.

This occurs only if the structure is

ductile (ie, if the legs can

squash)


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Ductile CollapseDuctile Collapse

540 lbs

135 lbs

135 lbs135 lbs

135 lbs

So small imperfections do not

matter, as long as the structuralelements are ductile

The forces in a hyperstaticstructure cannot be known

exactly, but this is not important

as long as we can predict thecollapse state


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Support ConditionsSupport Conditions

Roller Pin (hinge) Fixed


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Statically Determinate StructuresStatically Determinate Structures

! Simply supported beam

! Cantilever beam

! Three-hinged arch


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Statically Determinate

! Simply supportedbeam

! Cantilever beam

! Three-hinged arch

! Three-hinged frame

Indeterminate (hyperstatic)

! Continuous beam

! Propped cantilever beam

! Fixed end arch

! Rigid frame


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Continuous BeamContinuous Beam

! How many unnecessary supports?

! What is the degree of static indeterminacy?

Introduction to ESA

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