Problem 3-30/3-31/3-32/ Engineering Mechanics Materials.

Engineering Mechanics problem with solution.
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3–30. The lap joint is connected together using a 1.25 in. diameter bolt. If the bolt is made from a material having a shear stress–strain diagram that is approximated as shown,
determine the shear strain developed in the shear plane of the bolt when P = 75 kip.

3–31. The lap joint is connected together using a 1.25 in. diameter bolt. If the bolt is made from a material having a shear stress-strain diagram that is approximated as shown, determine the permanent shear strain in the shear plane
of the bolt when the applied force P = 150 kip is removed.

3–32. A shear spring is made by bonding the rubber annulus to a rigid fixed ring and a plug. When an axial load P is placed on the plug, show that the slope at point y in the
rubber is dy/dr = -tan g = -tan1P/12phGr22. For small angles we can write
dy/dr = -P/12phGr2. Integrate this
expression and evaluate the constant of integration using the condition that
y = 0 at r = ro. From the result compute
the deflection y = d of the plug.

[hugolebohec]

Sorry! Wouldn't the shear stress be 61.12 because the P is 150? The division of two disappears in making the equation of area hold a pi/4 to holding a pi/2 ?