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MECHANICS OF MATERIALS Course B-4

PROBLEMS Seely: Art. 132-135

CURTISS-WRIGHT ENGINEERING CADETTES 24D-A-137

24D-1. Each of the sections in Fig. 24D-1 represent the cross section of a cantilever beam carrying a vertical concentrated load through the shear center at the free end. Indicate the direction of the shearing force, if any, developed parallel to the long side in each rectangle of the section, as illustrated for the channel.

24D-2. Determine the deflection of the end of the streamline tubing in Problem 23D-1.

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MECHANICS OF MATERIALS Course B-4

REVIEW PROBLEMS Seely

CURTISS-WRIGHT ENGINEERING CADETTES- 32DO-A-149

32D0-1. Construct shear and moment diagrams for the beam loaded as shown in Fig. 32D0-1.

32D0-2. A 50-in. diameter boiler is made of steel plate 1/2 in. in thickness. The boiler is subjected to an internal pressure of 110 p.s.i. The longitudinal seam is a double riveted butt joint with a single 9/16-in. splice plate. The outside rows of rivets have a pitch of 6 in. and the inner rows a pitch of 3 in. The rivets are 7/8 in. in diameter. Determine the average shearing and bearing unit stresses, and also the average tensile unit stresses at both net sections of the main plate.

32D0-3. A cantilever beam has a cross-section as shown in Fig. 32D0-3. The beam is 8-ft. long and has a concentrated load of 600 lb. acting along the x-x axis at the free end.

(a ) Determine the maximum fiber stress in the beam.

(b) Determine the maximum deflection in the beam.

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CURTISS-WRIGHT ENGINEERING CADETTES- 32D0-A-149

32D0-4. Determine the shearing stress on the rivet which carries the greatest load in the connection indicated in Fig. 32D0-4. All rivets are 5/16 in. in diameter and are in single shear.

32D0-5. An airplane engine develops 1400 h.p. and is turning over at the rate of 1800 r.p.m. The hollow drive shaft has an outside diameter of 4 in. and an inside diameter of 3 in. The propeller has an efficiency of 80%. If the airplane is traveling in horizontal, level, steady flight at 240 m.p.h. determine the normal and shearing unit stresses in the propeller shaft at the end of a horizontal diameter on a plane that makes an angle of 30° with the horizontal.

32D0-6. Member DG in the truss shown in Fig. 32D0-6 (a) is a 1 1/2 by 1/4-in. 1025 steel angle, the properties of which are indicated in Fig. 32D0-6 (b). The effective length of the member is 46 in. and the fixity factor may be assumed to be 2.0. The 1 1/2 in. leg is to be welded to a gusset plate at each end. Design a welded connection which will develop the full strength of the member when DG is in compression. Refer to ANC-5 for allowable loads on welded seams.

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Mechanics of Materials Course B-4

Final Examination (10432) Seely

Curtiss-Wright Engineering Cadettes 33D-G-150

Note: Show all work, including scratch work in blue book. Original questions need not be copied in blue book.

1. (a) The proportional limit of a material is defined as ___________ (b) Define the coefficient of thermal expansion. (c) Define modulus of rupture as applied to a beam. (d) Give a reasonable value for the modulus of elasticity of Douglas fir or white pine. (e) Define shear center. (f) What is a principal axis? (g) Draw the conjugate beams for the beams shown in Fig. 1 (g) showing end conditions only (no M/EI loads). (h) Figure 1 (h) indicates a shaft coupling. What is the relationship between the unit shearing stresses in the bolts in the two bolt circles? (i) The direction of the neutral axis of the cross section of a beam subjected to unsymmetrical bending is dependent upon three factors. Name them. (j) Give the formula for evaluating the unit shearing stress in a beam. Define, explain, or illustrate the significane of each term.

2. A hollow steel propeller shaft with an outside diameter of 3 1/2 in. and a 1/4-in. wall thickness transmits a torque of 4,000 Ft. lbs. The shaft is 5 ft. long, E = 30(10)6 p.s.i and G = 12 (10)6 p.s.i. Determine

(a) The maximum unit shearing stress.

(b) The magnitude of the angle of twist in radians.

3. (a) Draw the shear and moment diagrams for the beam shown in Fig. 3 (a). (b) If the beam has a cross section as shown in Fig. 3 (b) determine the maximum fiber unit stress.

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Curtiss-Wright Engineering Cadettes 33D-G-150

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4. Two .081-in. 17S-T aluminum alloy sheets are connected by means of a triple riveted lap joint, a portion of which is shown in Fig. 4. The rivets are 1/4 in. in diameter and the allowable stresses are Ft = 55,000 p.s.i., Fs = 30,000 p.s.i. and Fbr = 75,000 p.s.i. (a) Determine the efficiency of the joint. (b) Determine the maximum allowable load per repeating group of rivets which the joint will carry with a margin of safety of .15.

5. A 24S-T forging to be used as a column is shown in Fig. 5. The fixity factor with respect to the x-x axis is l, and with respect to the y-y axis is 2. The critica Li/p [rho] is 79.2, Fco = 50,000 p.s.i., K = 421 p.s.i., n=1, and E = 10,500,000 p.s.i. Determine the maximum axial load the column may be expected to carry.

6. The member shown in Fig. 6 has a solid circular cross section of radius r. Determine the minimum permissible radius of the member if the maximum tensile stress on Section A-A shall not exceed 20,000 p.s.i.

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Fig. 5

Fig. 6