Introduction to Machine Design

Lecture 3

Dr./ Ahmed Mohamed Nagib Elmekawy

March 3, 20161

AxialStress

2

Beamundertheactionoftwotensileforces

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Beamundertheactionoftwotensileforces

4

DeformationsofMembersUnderAxialLoading

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DeformationsofMembersUnderAxialLoading

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AxialStress

7

8

9

10

ShearingStress

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ShearingStress

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ShearingStress

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BearingStressinconnections

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BearingStressinconnections

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BearingStressinconnections

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• Calculate the average normal stress in the links connecting a) B and D b) C and E

TorsionStress

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TorsionStress

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TorsionStress

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TorsionStress

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AngleofTwist

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ShearingStrain

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ShearingStrain

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ShearingStrain

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ShearingStrain

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Torque

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Torque

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Torquestresssummary

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Shear Stress𝜏 = 𝐺𝛾= %&' =

()%*,-

𝜏 : Shear Stress 𝑐: shaft radius𝐺: Modulus of rigidity 𝑑: Shaft diameter𝛾: Shear Strain𝐽 : Polar moment of inertiaFor a hollow circular shaft of inner radius c1 and outer radius c2,the polar moment of inertia is

∅: Angle of Twist

TorsionofaShaftwithCircularCross-Section

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TorsionofaShaftwithCircularCross-Section

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TorsionofaBeamwiththeSquareCross-Section

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TorsionofaBeamwiththeSquareCross-Section

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Example

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Example

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Example

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Example

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Example

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Example

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Example

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BendingStress

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BendingStress

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BendingStress

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BendingStress

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BendingStress

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BendingStress

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BendingStress

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BendingStress

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BendingStress

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BendingStress

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BendingStress

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BendingStress

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BendingStress

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BendingStress

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BendingStress

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BendingaCantileverBeamunderaConcentratedLoad

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BendingaCantileverBeamunderaConcentratedLoad

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BendingStress

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BendingStress

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BendingStress

59

BendingStress

60

BendingStress

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BendingStress

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BendingStress

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BendingofCurvedbeam

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Displacement Stress in x direction

Example

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Example

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