Hafiz Kabeer Raza Research Associate

Faculty of Materials Science and Engineering, GIK Institute Contact: Office G13, Faculty Lobby

raza@giki.edu.pk, hkabeerraza@gmail.com, 03344025392

MM222

Strength of Materials

Lecture 23

Spring 2015

Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials

Problem 4.1

Important: how to calculate d and y

Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials

Problem 4.11

Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials

Bending of Members Made of Several Materials Consider a composite beam formed from

two materials with E1 and E2.

Normal strain varies linearly.

yx

Piecewise linear normal stress variation.

yEE

yEE xx

222

111

Neutral axis does not pass through

section centroid of composite section.

Elemental forces on the section are

dAyE

dAdFdAyE

dAdF

2221

11

1

2112

E

EndAn

yEdA

ynEdF

Define a transformed section such that

xx

x

n

I

My

21

Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials

Example 4.03

Bar is made from bonded pieces of

steel (Es = 29x106 psi) and brass

(Eb = 15x106 psi). Determine the

maximum stress in the steel and

brass when a moment of 40 kip*in

is applied.

SOLUTION:

Transform the bar to an equivalent cross

section made entirely of brass

Evaluate the cross sectional properties of

the transformed section

Calculate the maximum stress in the

transformed section. This is the correct

maximum stress for the brass pieces of

the bar.

Determine the maximum stress in the

steel portion of the bar by multiplying

the maximum stress for the transformed

section by the ratio of the moduli of

elasticity.

Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials

Example 4.03

Evaluate the transformed cross sectional properties

4

3

1213

121

in 063.5

in 3in. 25.2

hbI T

SOLUTION:

Transform the bar to an equivalent cross section

made entirely of brass.

in 25.2in 4.0in 75.0933.1in 4.0

933.1psi1015

psi10296

6

T

b

s

b

E

En

Calculate the maximum stresses

ksi 85.11

in 5.063

in 5.1inkip 404

I

Mcm

ksi 85.11933.1max

max

ms

mb

n

ksi 22.9

ksi 85.11

max

max

s

b

Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials

Problem 4.41