Shear stress versus shear strain

For homogeneous & isotropic materials pure shear causes angular distortion of a material as shown above.

Pure shear is most often studied by torsional tests of thin bars. Behavior is completely analogous to normal stresses.

Shear stress-strain diagram

G

)1(2

EG

G is shear modulus or modulus of rigidity

The shear stress-strain diagram for a titanium alloy bar tested in torsion is shown in the Figure. Determine

i) Shear modulus

ii) Proportional Limit

iii) Ultimate stress

iv) Yield stress

v) Fracture stress

A bearing pad used to support machines is shown. The following formulae can be used to determine shear stress, shear strain and displacement.

ab

Vaver

abG

V

Gaver

abG

Vhhd tantan

abG

hVhd

For small angles

Problem (4): The plastic block shown of 50 mm depth is bonded to a rigid support and to a vertical plate to which a 240-kN load P is applied. Knowing that for the plastic used G=1000 MPa, determine the deflection of the plate.

P

120 mm

80 mm

P

120 mm

80 mm

P

120 mm

80 mm

P

120 mm

80 mm

Spring 2006 Mid Term Question

Rigid support

Problem (4): The plastic block shown of 50 mm depth is bonded to a rigid support and to a vertical plate to which a 240-kN load P is applied. Knowing that for the plastic used G=1000 MPa, determine the deflection of the plate.

P

120 mm

80 mm

P

120 mm

80 mm

P

120 mm

80 mm

P

120 mm

80 mm

Spring 2006 Mid Term Question

Rigid support

MPaab

Vaver 40

12.0*05.0

000,240

radsGaver 04.0

1000

40

mmhd 2.304.0*80

Allowable Stress

allow

failSF

..

allow

failSF

..F.S.=1

F.S.=3

Factor of safety

..SFfail

allow

..SFfail

allow

Designing for allowable stress

allow

PA

allow

VA

Tension

Bearing (compression)

Shear

Problem (6): Determine the intensity w of the maximum distributed load that can be supported by the hanger assembly so that an allowable shear stress of allow = 15 ksi is not exceeded in the 0.40-in.-diameter bolts at A and B, and an allowable tensile stress of σallow = 25 ksi is not exceeded in the 0.5-in.-diameter rod AB.

Spring 2006 Mid Term Question Solve at home – will cover in help session on Sept 7th