STRUCTURAL ANALYSIS

Instructor: Muhammad Haroon

Assistant Professor,

Civil Engineering Department,

Wah Engineering College,

University of Wah Wah Cantt

Course Code: CE-302

Credit hours: 3+1

INTRODUCTION

Reference Books

Structural Analysis by R.C. Hibbeler

Pentice Hall

Indeterminate Structural Analysis by Chu Kia Wang

McGraw Hill

Analysis of Structures by West, H.H.

John Wiley and Sons

Class Decorum

The person who will not be serious will be treated accordingly

Late comers will not be allowed

Mobile phones are must to be kept silent

Class participation is encouraged

Course Grading

4 Quizzes 7.5%

4-6 Assignments 7.5%

Mid Term Exam 15%

Final Exam 37.5%

Practicals 15%

Project 7.5%

Viva 10%

What is a Structure?

A structure is a system of connected parts used to support a load.

Elements/Parts of a Structure

Some of common elements from which structures are composed are

as follows:

Tie Rods / Struts

Structural members subjected to a tensile force are often referred to

as tie rods or bracing struts.

Beams

Beams are usually straight horizontal members used primarily to

carry vertical loads.

Tapered Beams

When the cross-section varies the beam is referred to as tapered or

haunched.

Built-up Sections

Beam cross-sections may also be built-up by adding plates to their

top and bottom. Such sections are known as built-up sections.

Plate Girder

When the span and loads are very large, cross-sections are fabricated

by using a large plate for the web and welding or bolting plates to its

ends for flanges, known as plate girder.

Columns

Members that are generally vertical and resist axial compressive

loads are referred to as columns.

Occasionally, columns are subjected to both an axial load and a

bending moment. These members are referred to as beam-columns.

Column Beam column

Types of Structures

Frames

Frames are normally used in buildings.

They are composed of beams and columns connected by pinned or

fixed ends.

Trusses

Trusses are composed of slender straight members connected at their

ends by hinged connections in a triangular fashion. The members are

either in uniform tension or compression.

When the span of a structure is large, and depth is not an important

criterion for design, a truss may be selected.

10/9/2013

http://upload.wikimedia.org/wikipedia/commons/5/5c/Grammene-vierendeelbridge_20030618.jpg

Cables and Arches

For Long span distances, cables and arches can be used.

Cables are usually flexible and carry their loads in tension.

Arch supports their loads in compression.

Arches are frequently used in bridge structures, dome roofs, and for

openings in masonry walls.

Triangular Arch Round Arch Segmental Arch

Rampant Round

Arch Lancet Arch Shoulder Flat

Arch Three-Foiled

Cusped Arch

Equilateral

Pointed Arch

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Horseshoe Arch Three-centered

Arch

Elliptical Arch

Inflexed Arch Ogee Arch Reverse Ogee

Arch Tudor Arch

Parabolic Arch

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Surface/shell Structures

These are made from materials having a very small thickness

compared to its other dimensions.

These structures are difficult to analyze, due to three dimensional

geometry of their surface.

Loads

The loads on a structures are determined after finding the structural

dimensions.

The loads define the type of structure to be constructed.

Once the structural form has been decided, the actual design begins.

Types of Loads

Dead Loads

Live Loads

Bridge Loads

Wind Loads

Earthquake Loads

Hydrostatic and Soil Pressure

Other Natural Loads

What is Structural Analysis?

What is Structural Design?

The design of structure starts with those elements

which are subjected first to the primary loads.

For example, first the slabs are designed then beams,

then columns and then footing.

Loads are specified in:

General Building Codes

Design Codes

IMPORTANT!

The ultimate responsibility for the design lies with the structural

engineer.

Equations of Equilibrium

The structure or its member is in equilibrium when it maintains a

balance of force and moment.

0 0 0

0 0 0

zyx

zyx

MMM

FFF

Equations of Equilibrium

The principal load-carrying portions of most structures lie in a single

plane, and since the loads are also coplanar, the above requirements

for equilibrium reduces to

0

0

0

M

F

F

y

x

Internal Loadings

In general, the internal loadings acting at the cut section of the

member will consist of a normal force N, shear force V, and bending

moment M.

V

N

M V

N

M

Determinacy

When all the forces in a structure can be determined from the

equilibrium equations, the structure is referred to as statically

determinate.

When the unknown forces in a structure are more than the available

equilibrium equations, that structure is known as statically

indeterminate.

Determinacy

If there is a total of n parts and r force and moment reaction

components, we have

r = 3n statically determinate

r > 3n statically indeterminate

Stability

A structure will be geometrically unstable (it will move slightly or

collapse) if

there are fewer reactive forces than equations of equilibrium or

there are enough reactions and instability will occur if the lines of

action of reactive forces intersect at a common point or are parallel to

one another.

Stability

r < 3n unstable

r 3n unstable if member reactions are concurrent or parallel

or some of the components form a collapsible mechanism

Statically Indeterminate Structures (SIS)

When the unknown forces in a structure are more than the available

equilibrium equations, that structure is known as statically

indeterminate.

Most of the structures designed today are statically indeterminate.

This indeterminacy may be due to the added supports or members, or

by the general form of the structure.

Advantages of SIS

Smaller Stresses

Greater Stiffness

Redundancies

P

P

8max

PLM

4max

PLM

49

w

EI

wL

384

4

max

w

EI

wL

384

5 4

max

Advantages of SIS

Smaller Stresses

Greater Stiffness

Redundancies

Statically determinate beam

Internal hinge

Statically unstable

Advantages of SIS

Smaller Stresses

Greater Stiffness

Redundancies

Statically indeterminate beam

Internal hinge

Statically stable

Disadvantages of SIS

Stress due to Support Settlement

Stress due to Temperature Changes and Fabrication Errors

Statically indeterminate beam

Disadvantages of SIS

Stress due to Support Settlement

Stress due to Temperature Changes and Fabrication Errors

Statically determinate beam

Disadvantages of SIS

Stress due to Support Settlement

Stress due to Temperature Changes and Fabrication Errors

Statically indeterminate beam

METHODS OF

ANALYSIS

TYPES OF METHODS There are two type of methods for Statically

Indeterminate Structures

Displacement Method:

Slope Deflection Method

Moment Distribution Method

Force Method:

Method of least work (Unit load method)

Method of consistent deformation

FEM VALUES CHART