MM222 Lec 19-20

Hafiz Kabeer Raza Research Associate

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

[email protected], [email protected], 03344025392

MM222

Strength of Materials

Lecture – 19

Spring 2015

The actual value of T is 420 lb.ft

Spring 2015 By Hafiz Kabeer Raza MM222 Strength of Materials

Design of Transmission Shafts • Principal transmission shaft

performance specifications are:

- power

- speed

• Determine torque applied to shaft at

specified power and speed,

f

PPT

fTTP

2

2

• Find shaft cross-section which will not

exceed the maximum allowable

shearing stress,

shafts hollow2

shafts solid2

max

41

42

22

max

3

max

Tcc

cc

J

Tc

c

J

J

Tc

• Designer must select shaft

material and cross-section to

meet performance specifications

without exceeding allowable

shearing stress.


Example


Problem 3.70

• Use T/τmax = J/c2

Hafiz Kabeer Raza Research Associate

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

[email protected], [email protected], 03344025392

MM222

Strength of Materials

Lecture – 20

Spring 2015


Chapter 4

Pure Bending


Pure Bending

Pure Bending: Prismatic members

subjected to equal and opposite couples

acting in the same longitudinal plane


Other Loading Types

• Eccentric Loading: Axial loading which

does not pass through section centroid

produces internal forces equivalent to an

axial force and a couple

• Transverse Loading: Concentrated or

distributed transverse load produces

internal forces equivalent to a shear

force and a couple


Symmetric Member in Pure Bending

• Internal forces in any cross section are equivalent

to a couple. The moment of the couple is equal

to the bending moment of the section.

• From statics, a couple M consists of two equal

and opposite forces.

• The sum of the components of the forces in any

direction is zero.

• The moment is the same about any axis

perpendicular to the plane of the couple and

zero about any axis contained in the plane.


Bending Deformations Beam with a plane of symmetry in pure

bending:

• member remains symmetric

• bends uniformly to form a circular arc

• cross-sectional plane passes through arc center

and remains planar

• length of top decreases and length of bottom

increases

• a neutral surface must exist that is parallel to the

upper and lower surfaces and for which the length

does not change

• stresses and strains are negative (compressive)

above the neutral plane and positive (tension)

below it


Tensile and Compression


Strain Due to Bending Consider a beam segment of length L.

Where:

ρ = radius of curvature (length from center of

curvature to the neutral axis)

θ = the angle subtended by the entire length after

bending

y = the distance of the point where stress/strain is to

be computed from neutral axis (0, c)

After deformation, the length of the neutral surface

remains L. Length at other sections above or below,

mx

m

m

x

c

y

cρ

c

yy

L

yyLL

yL

or

linearly) ries(strain va


Stress Due to Bending • For a linearly elastic material,

linearly) varies(stressm

mxx

c

y

Ec

yE

I

My

c

y

inertiaofmomenttionII

Mc

c

IdAy

cM

dAc

yydAyM

x

mx

m

mm

mx

ngSubstituti

sec,

2


Beam Section Properties • The maximum normal stress due to bending,

modulussection

inertia ofmoment section

c

IS

I

S

M

I

Mcm

A beam section with a larger section modulus

will have a lower maximum stress

• Consider a rectangular beam cross section,

Ahbhh

bh

c

IS

613

61

3

121

2

Between two beams with the same cross

sectional area, the beam with the greater depth

will be more effective in resisting bending.

• Structural steel beams are designed to have a

large section modulus.

MM222 Lec 19-20

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