Indian Institute of Technology - Tirupati
ME207L MECHANICS OF SOLIDS
Topic: Stress
Tutorial-2
1. The assembly consists of three disks A, B, and C that are used to support the load of
140 kN. Determine the smallest diameter d1 of the top disk, the diameter d2 within the
support space, and the diameter d3 of the hole in the bottom disk. The allowable
bearing stress for the material is σ allowable = 350MPa and allowable shear stress is
τallowable = 125 MPa.
2. If, P = 20KN, determine the average shear stress developed in the pins at A and C.
The pins are subjected to double shear as shown, and each has a diameter of 18 mm.
3. The joint is fastened together using two bolts. Determine the required diameter of the
bolts if the failure shear stress for the bolts τ fail = 350 MPa. Use a factor of safety 2.5
for shear.
4. The long bolt passes through the 30mm thick plate. If the force in the bolt shank is 8
kN, determine the average normal stress in the shank, the average shear stress
along the cylindrical area of the plate defined by the section lines a–a, and the
average shear stress in the bolt head along the cylindrical area defined by the section
lines b–b.
5. The bar in Figure has a constant width of 35 mm and a thickness of 10 mm.
Determine the maximum average normal stress in the bar when it is subjected to the
loading shown.
6. The hanger is supported using the rectangular pin. Determine the required thickness t
of the hanger, and dimensions a and b if the suspended load is P = 60 kN. The
allowable tensile stress is (σt)allow = 150 MPa,the allowable bearing stress is (σb)allow =
290 MPa, and the allowable shear stress is τ allow = 125 MPa.
7. The aluminum bracket A is used to support the centrally applied load of 8 kip. If it has
a constant thickness of 0.5 in., determine the smallest height h in order to prevent a
shear failure. The failure shear stress is τ fail = 23 ksi. Use a factor of safety for shear
of F.S. = 2.5.
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Tutorial-2 Stress
8. The d = 15 mm diameter solid rod shown in figure below passes through a D = 20
mm diameter hole in the support plate. When a load P is applied to the rod, the rod
head rests on the support plate. The support plate has a thickness of b = 12 mm. The
rod head has a diameter of a = 30 mm and the head has a thickness of t = 10 mm. If
the normal stress produced in the rod by load P is 225 MPa, determine
(a) The bearing stress acting between the support plate and rod
head. (b) The average shear stress produced in the rod head.
(c) The punching shear stress produced in the support plate by the rod
head.
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9. The steel pipe column shown in figure below has an outside diameter of 8.625 in. and
a wall thickness of 0.25 in. The timber beam is 10.75 in wide, and the upper plate has
the same width. The load imposed on the column by the timber beam is 80 kips,
determine
(a) The average bearing stress at the surfaces between the pipe column and the
upper and lower steel bearing plates.
(b) The length L of the rectangular upper bearing plate if its width is 10.75 in. and
the average bearing stress between steel plate and the wood beam is not to
exceed 500 psi.
(c) The dimension "a" of the square lower bearing plate if the average bearing
stress between the lower bearing plate and the concrete slab is not to exceed 900
psi.
