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Solid Mechanics

Task topic Torque:

Exercises 3.1 & 3.24

a) Find the maximum shear stress caused by a torque of 40 kips ¨ and the solid axle Aluminum 3 inch in diameter, shown below. b) Solve the subsection "a" assuming that the shaft has been replaced by a hole with the same outside diameter and 1 inch inside diameter.

c) Determine the angle of twist caused by a torque T of 40 kips ¨ and the aluminum shaft 3-inch diameter, shown in the figure below (G = 3.7 x 10 ⁶ psi). d) Solve the previous section assuming that the solid axle has been replaced by a hollow shaft with the same outside diameter and 1 inch inside diameter.

Exercise 3.2 & 3.23

a) Find the torque T causing a sharp maximum of 45 MPa the hollow cylindrical shaft shown below. b) find the same shear stress caused by the same torque on a solid shaft with the same cross-sectional area.

c) Find the torque T that gives rise to a torsion angle of 3 degrees in the hollow cylinder of steel shown in the figure below ( G = 77 GPa ) . d) Determine the angle of torque produced by the same torque T a solid cylindrical shaft of the same material and with the same cross section.

Exercises 3.3

applies a torque of 1.75 kN • m the solid cylinder of the figure below. Halle: a) the maximum shear, b) the percentage of torque taken by the kernel of 25 mm diameter.

Exercise 3.4

a) Find the torque to be applied to solid axle 3-inch diameter without exceeding allowable shearing of 12 ksi . b) Solve the subsection "a" assuming that it replaces a solid shaft hollow shaft of equal area and an inside diameter equal to half the outside.

Exercise 3.5 & 3.27

The torques shown in the figure below, are exerted on the pulleys A , B and C . If both axles are solid, find the maximum shear stress: a) on the axis AB , b) on the shaft BC.

The torques are illustrated in the figure are exerted on the pulleys A , B and C . Knowing that both axles are solid and made of brass (G = 39 GPa), torsion angle is in between: c) A and B , D) A and C .

Exercises 3.6 & 3.7

Normally application, the electric motor, shown below, has a torque of 12 kips ¨ and on E . Knowing that each axle is solid, find the maximum shear stress: a) on the shaft BC, b) on the shaft CD, c) in the axis of .

Now suppose we have drilled a hole 1 inch in diameter on each axis, find the maximum shear stress, d) on the shaft BC , e) on the shaft CD , f) on the axis of .

3.8 Exercises

The torques shown in the figure below, are exerted on the pulleys A , B, C and D . Knowing that the axles are solid, find: a) the axis on which occurs the maximum shear stress, b) the magnitude of that effort.

3.25 Exercises

Halle maximum permissible diameter of a steel bar of 10 foot length (G = 11.2 x 10 ⁶ psi), if the bar has to be subjected to a torsion angle of 90 degrees but not exceeding a shear stress of 15 ksi .

3.26 Exercises

While an oil well is being drilled at 2 500 m depth shows that the top of the drill pipe is used, 200 mm diameter steel ( G = 77 GPa ), rotating 2.5 revolutions before the piercing tip begins to operate. Find the maximum shear stress that causes the torque on the pipe.

Exercises 3.28 & 3.29

The electric motor, shown in the figure below, has a torque of 6 kips ¨ and the Aluminum shaft ABCD when rotated at constant speed. Knowing that G = 3.7 x 10 6 psi and torques exerted on the pulleys B and C are indicated in the figure, find the angle of twist between : a) B and C , b) B and D .

Now suppose a hole is drilled 1-inch in diameter around the axis, find the angle of twist between: c) B and C , d) B and D .

3.30 Exercises

The torques shown in the figure below, exerted on the pulleys A, B , C and D . If each axle is solid, 120 mm long and made of steel ( G = 77 GPa ), find the angle of twist between: a) A and C, b) A and E .

Exercises 3.31 & 3.32

solid shaft AB has a diameter d s = 1.5 in. and is made of steel with G = 11.2 x 10 ⁶ psi and t _adm = 12 ksi , while the CD sleeve is Brass with G = 5.6 x ^{10 6 psi} and adm t = 7 ksi . Find a) the maximum angle that can be rotated end A .

solid shaft AB has a diameter _{s d = 1.75} in. and is made of steel with G = 11.2 x 10 ⁶ psi and t adm = 12 ksi, while the CD sleeve Brass is G = 5.6 x 10 ⁶ psi and t = adm 7 ksi. Halle: b) the maximum torque T that can be applied if A should not exceed the allowable stresses given and if the angle of twist of the CD sleeve should not exceed 0.375 °. c) the corresponding rotation angle end A .

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Task 8

Warps Task cutting theme:

Exercises 2.82 & 2.83

A vibration isolation unit consists of 2 blocks hard rubber plate attached to an AB and rigid as shown in the figure below. Knowing that a force P = 6 Kips cause deflection d = 1 / 16 inch plate AB, find the modulus of the rubber used.

A unit Vibration isolation consists of 2 blocks of hard rubber with a modulus G = 2.75 ksi attached to a plate and rigid AB, as shown in the figure above. P calling the magnitude of the applied force on the plate and d the corresponding deflection, find the effective spring constant P / d the system.

Exercises 2.84 & 2.85

plastic block shown in the figure is attached to the rigid support and a vertical plate, which applies a force P of 240 kN . Knowing that the plastic used G = 1050 MPa , find a) the deflection of the plate, b) P load to be applied to produce a deflection of 1.5 mm .

Exercises 2.86 & 2.87

Two rubber blocks G = 1.75 ksi are attached to rigid and AB plate, as shown in the figure below. Knowing that c = 4 in. and P = 10 kips , find the minimum allowable size and to block b if the shear in the rubber must not exceed 200 psi and deflection of the plate should be at least 0.1 inches .

Two rubber blocks G = 1.50 ksi are attached to rigid supports and a plate AB, as shown in the figure above. Knowing that b = 8 in. and c = 5 in. , determine the maximum permissible load P and the minimum thickness permissible to block if the shear in the rubber should not exceed 210 psi and deflection of the plate should be at least ¼ inch .

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Solid Mechanics Solid Mechanics Task 7 Task 6 Mechanical

Task topic Poisson Ratio:



Exercises 2.66 & 2.67

In a stress test is subjected Aluminum bar 20 mm in diameter with a force voltage P = 30 kN. Knowing that E = 70 GPa, and n = 0.35, determine a) the elongation of the rod in a length of 150 mm, b) the change in the diameter of the bar.

In a standard test voltage undergoes an experimental plastic rod 20 mm in diameter with a force P = 6 kN. Knowing that it detects an elongation of 14 mm and a decrease in the diameter of 0.85 mm at a measuring length of 150 mm, determine the modulus of elasticity, stiffness and Poisson's ratio of material.

Exercise 2.68


A line with slope 4:10 was recorded in a yellow brass plate 6 "wide and ¼ inch thick. Using data from Appendix B , find the slope of the line when the plate is subjected to an axial force of 45 kips, as shown below.

Exercise 2.69


A steel pipe 6 feet long, 12 inches outside diameter and ½ inch thick, is used as a short column to support an axial load of 300 kips. Using data from Appendix B for structural steel, find a) the change in length of the pipe, b) the change of outside diameter, c) the change in thickness of the pipe.

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Task topic

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Task 5 Solid

Statically Indeterminate Problem:

Exercise 2.33

A concrete pole (shown in the figure below) of 4 feet is reinforced with steel bars 4 ¾ inch in diameter. If E _s ^{= 29 x 10 6 psi and} c E = 3.6 x ⁶ 10 psi, find the normal stresses in the steel and concrete when applied to Post an axial load of 150 kips.

Exercises 2.34 & 2.35

A bar of 250 mm with 15- SECTIONS x 30 mm consists of 2 layers of aluminum 5 mm, together to a central brass of the same thickness. If it is subjected to axial loads P = 30 kN and knowing that E _Al = 70 GPa and E _L = 105 GPa, find the normal stress a) Aluminum b) in the brass c) the extension of the bar made if the axial load P is 45 kN.

Exercise 2.36

apply compressive force of 40 kips, thrust, on both ends of the assembly shown below, terminals through rigid plates. Knowing that E _s = 29 x ^{10 6 psi and E} _to = 10 x 10 6 psi, find: a) normal stresses in the steel core and Aluminum housing, b) distortion of the whole.

Exercise 2.37

A plastic rod which consists of two parts cylindrical AB and BC is restricted at both ends and carries a sack of 6 kips, as shown in the figure below. Knowing that E = 0.45 x 10 6 psi, find: a) reactions in A and C, b) the normal stress on each portion of the bar.

Exercises 2.38 & 2.39

Two cylindrical rods , a steel and brass the other, are united in C and have rigid in A and E . Given the load shown in the figure below and knowing that E s = 200 GPa and E b = 105 GPa, find: a) reactions and A E, b) the deflection of point C .

Now suppose that the bar is Brass AC and EC bar Steel is, find: c) reactions and A E, d) the deflection of point C .

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