Homework 2
Mechanics of Materials
Name: _________________________________________________________ Hour of class: ________
1. The leaned lever represented in the image is in equilibrium:
a. Find the diameter of the AB bar if the normal stress is limited to 100 MPa.
b. Find the shear stress in the pin placed in D, with 20 mm of diameter.
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Homework 2
Mechanics of Materials
Name: _________________________________________________________ Hour of class: ________
2. A load P is applied to a steel rod supported, as shown in the figure, for an aluminum plate
where has been drilled a hole with 6 in of diameter. Knowing that the shear stress should not
exceed 18ksi in the steel rod and 10ksi in the aluminum plate, calculate the maximum load P
that can be applied to the rod.
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Homework 2
Mechanics of Materials
Name: _________________________________________________________ Hour of class: ________
3. The support wheel stays in its place under the leg of a scaffold by means of a pin of 4 mm of
diameter as shown in the figure. If the wheel is submitted to a normal force of 3 KN, determine
the average shear stress generated in the pin. Slight the friction.
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Homework 2
Mechanics of Materials
Name: _________________________________________________________ Hour of class: ________
4. The union that is shown in the figure is composed of five plates of steel, each one with 5 mm in
thickness, united by a single bolt with 6 mm of diameter. The load transferred among the plates
is of 6,000 N distributed as shown.
a. Calculate the greater shear stress in the bolt, without taking into account the friction
among the plates.
b. Calculate the largest bearing stress acting in the bolt.
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Homework 2
Mechanics of Materials
Name: _________________________________________________________ Hour of class: ________
5. A hydraulic punch with a capacity of 500 kN makes round holes on an aluminum plate of 10
mm of thickness. If the shear stress resistance of this plate is of 250 MPa. What is the maximum
diameter of the hole that can be punched?
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Homework 2
Mechanics of Materials
Name: _________________________________________________________ Hour of class: ________
6. Two bars of rectangular cross sections, thickness t of 5/16 in, are joined by a bolt as shown in
the figure, the permissible shear stress in the bolt is of 12,000 psi and the permissible bearing
stress between bolt and bars is 20,000 psi. If the force of tension P is 1,800 lbs. What is the
minimum necessary diameter of the pin?
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Homework 2
Mechanics of Materials
Name: _________________________________________________________ Hour of class: ________
7. In the figure is shown the outline of armor (a) and the sketch (b) of the detail on the union of the
bars through a joint plate at point B.
a. How many rivets of 19 mm in diameter are needed to unite the BC bar to the plate, if the
permissible stresses are in shear 70 MPa and bearing 140 MPa?
b. How many for the bar BE?
c. What is the normal stress compression or tension in BC and BE?
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Homework 2
Mechanics of Materials
Name: _________________________________________________________ Hour of class: ________
8. Three pieces of wood are joined with bolts, to make a column. The diameter of each bolt is ½ in
and the inner diameter of each washer is 5/8 in, the diameter of the washer is a little bigger than
the diameter of the hole in the wood. Determine the minimum outer diameter in the washers,
knowing that the limit normal stress in the bolts is 5 ksi and the bearing stress between the
washers and the wood cannot exceed 1.2 ksi.
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Homework 2
Mechanics of Materials
Name: _________________________________________________________ Hour of class: ________
9. The post of oak (60 x 60 mm) is supported by the block of pine, if the permissible bearing stress
for these materials is 43 MPa and 25 MPa respectively, determine the maximum load that they
can support. If a stiff plate is placed between the two materials, determine its required area so
that the maximum load can be borne, what value has this load?
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Homework 2
Mechanics of Materials
Name: _________________________________________________________ Hour of class: ________
10. Two forces are applied to the bracket BCD as shown. The pin at C is to be made of steel having
a maximum shearing stress of 350 MPa, determine:
a. The diameter of the pin at C.
b. The required thickness of the bracket supports at C, knowing that the allowable bearing
stress of the material used is 300 MPa.
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