strength of material chapter 1

8/7/2019 strength of material Chapter 1

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PPB 25403 Strength of Materials

Lecture 1: Stress Analysis
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Mechanics of Materials: An Introduction

What?

Why?

Applications?


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Introduction

Mechanics of materials is a study of the relationshipbetween the external loads on a body and the intensityof the internal loads within the body.

This subject also involves the deformations and stability

of a body when subjected to external forces.

Applications:

Complete picture of mechanical behaviour such as

forces, motion Safe design in all type of structures i.e building, bridges,

airplanes, ships, motors, machines.


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Learning Outcomes

Stress

Review of Free Body Diagram

Equilibrium of a Deformable Body

Stress Concept

Normal and Shear Stresses

Factor of Safety


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External Forces1.Surface Forces

- caused by direct

contact of otherbodys surface

2.Body Forces- other body exerts a force

without contact


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ReactionsSurface forces developed at the

supports/points of contact between bodies.


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Equations of EquilibriumEquilibrium of a body requires a balance

of forcesand a balance of moments

For a body with x, y, zcoordinate systemwith origin O,

Best way to account for these forces isto draw the bodys free-body diagram(FBD).

0M0FO

0,0,0

0,0,0

zyx

zyx

MMM

FFF


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Internal Resultant LoadingsObjective of FBD is to determine the resultant

force and moment acting within a body.

In general, there are 4 different types ofresultant loadings:

a) Normal force, N

b) Shear force, Vc) Torsional moment or torque, T

d) Bending moment, M


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Stress

Distributionof internal loading is important inmechanics of materials.

We will consider the material to be continuous.

This intensityof internal force at a point iscalled stress.


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Stress

Normal Stress

Force per unit area acting normal toA

Shear Stress

Force per unit area acting tangent toA

A

FzA

z0

lim

A

F

A

F

y

Azy

x

Azx

0

0

lim

lim


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Average Normal Stress in an Axially Loaded Bar

When a cross-sectional areabar is subjectedto axial force through the centroid, it is onlysubjected to normal stress.

Stress is assumed to be averaged over the area.


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Average Normal Stress in an Axially Loaded Bar

Average Normal Stress DistributionWhen a bar is subjected to a

constant deformation,

Equilibrium 2 normal stress components

that are equal in magnitudebut opposite in direction.

A

P

AP

dAdFA

= average normal stressP = resultant normal forceA = cross sectional area of bar


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Example 1

The bar has a constant width of 35 mm and a thickness of 10 mm. Determine the

maximum average normal stress in the bar when it is subjected to the loadingshown.

Solution:By inspection, different sections have different internal forces.


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Solution:

By inspection, the largest loading is in region BC,

kN30BCP

Since the cross-sectional area of the bar is constant,

the largest average normal stress is

(Ans)MPa7.8501.0035.0

10303

A

PBCBC


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Average Shear Stress

The average shear stressdistributedover each sectioned area that develops ashear force.

2 different types of shear:

A

Vavg

= average shear stressP = internal resultant shear forceA = area at that section

a) Single Shear b) Double Shear


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Allowable Stress

Many unknown factors that influence theactual stress in a member.

A factor of safetyis needed to obtained

allowable load.The factor of safety(F.S.) is a ratio of the

failure load divided by the allowable load

allow

fail

allow

fail

allow

fail

SF

SF

FFSF

.

.

.


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What we have learned today

Free Body Diagram


Stress Concept

Normal and Shear Stresses

Factor of Safety

strength of material chapter 1

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