Practice Problems Fourth Test 1. A single horizontal force P of magnitude 150 lb is applied to the lever as shown. If the diameter DAB = 1.2 in, determine a) the normal and shearing stresses on an element located at point H with sides parallel to x and y axes, b) the principal planes and the principal stresses at point H. Ans. σmax =13.52 ksi, σmin = - 4.68 ksi. 2. A steel pipe of 12 in outer diameter is fabricates from ¼–in thick plate by welding along a helix that forms an angle of 22.5o with a plane perpendicular to the axis of the pipe. Knowing that a 40 kip axial force P and 80 kip–in torque T, each directed as shown, are applied to the pipe, determine σ and τ in directions normal and tangential to the weld. Ans. σ = -4.76 ksi, τ = - .467 ksi. 3. Two steel plates of uniform cross section 10 × 80 m are welded together as shown. Knowing that centric 100 kN forces are applied to the welded plates and that β = 25o, determine (a) the in-plane shearing stress parallel to the weld, (b) the normal stress perpendicular to the weld. Ans. 47.9 MPa, 102.7 MPa. 4. Two steel plates of uniform cross section 10 × 80 m are welded together as shown. Knowing that centric 100 kN forces are applied to the welded plates and that the in-plane shearing stress parallel to the weld is 30 MPa, determine (a) the angle β, (b) the corresponding normal stress perpendicular to the weld. 5. A 400 lb vertical force is applied at D to a gear attached to the solid 1 in diameter shaft AB. Determine the principal stresses and the maximum shearing stress at point H located as shown on top of the shaft. Ans. 25.1 ksi, -.661 ksi, 12.88 ksi. 6. The steel pipe AB has a 102 mm outer diameter and a 6 mm wall thickness. Knowing that arm CD is rigidly attached to the pipe, determine the principal stresses and the maximum shearing stress at point K. Ans. 12 MPa, -48.7 MPa, 30.5 MPa. 7. A tray rests on an extendible arm consisting essentially of two steel tubes of different outer diameters. The downward force is applied at the tray center F0 = 1000 N. Determine the stresses at the point of tube 1 where the bending and torsional stresses are greatest. Draw the Mohr’s circle for that stress state. Both members have a wall thickness of 4 mm. d1 = 40 mm, d2 = 34 mm, a = 700 mm, and b = 500 mm. Ans. σavg = 94:35 MPa, τmax = 115.9 MPa. 8. A road sign consists of a steel post AB that has an outer diameter of 16 in., a wall thickness of 0.75 in., and a length of 25 ft. The pole BC has an outer diameter of 12 in., a wall thickness of 0.625 in., and a length of 40 ft to the center of the sign. The sign is 15 ft wide by 10 ft high and is subjected to a wind pressure of 0.2 psi. Determine the largest stresses in the vertical post AB due to the wind pressure, and draw Mohr’s circle for that stress state. Ans. σavg = 4950 psi, τmax = 9340 psi. 9. The T-beam is made from two plates welded together as shown. Determine the maximum uniform distributed load w that can be safely supported on the beam is the allowable bending stress is σallow = 150 MPa and the allowable shear stress is τallow = 70 MPa. Ans. 10.8 kN/m 10. Determine the minimum depth h of the beam to the nearest multiples of 5 mm that will safely support the loading shown. The allowable bending stress is σallow =147 MPa and the allowable shear stress is τallow = 70 MPa. The beam has an uniform thickness of 75 mm. Ans. h = 230 mm The following are the practice problems corresponding to chapter 12. This topic will be covered in Final Exam. 11. For the beam and loading shown, determine (a) the equation of the elastic curve for portion AB of the beam, (b) the deflection at midspan, and (c) the slope at B. Ans. b) –woL4/256EI, c) woL3/120EI. 12. For the beam and loading shown, determine (a) the equations of the elastic curve, (b) the deflection C. P = 35 kips, E = 29 × 106 psi, I = 291 in4. Ans. (b) 0.398 in 13. For the beam and loading shown, knowing that a = 2m, w = 50 kN/m, E = 200 GPa, and I = 84.9 × 106 mm4, determine (a) the equations of the elastic curve, (b) the slope at A, (c) the deflection at C. 14. Using the method of superposition determine the slope and the deflection of the beam at the free end. EI is constant. Ans. PL2/EI, – 17PL3/24EI. 15. Using the method of superposition determine the slope and the deflection of the beam at the free end. EI is constant. Ans. –5PL2/8EI, –7PL3/16EI. 16. Using the method of superposition determine the slope and the deflection of the beam at the free end. EI is constant. Ans. –PL2/24EI, –PL3/48EI. 17. Using the method of superposition determine the slope and the deflection of the beam at the free end. EI is constant, M = wL2/24. Ans. wL3/48EI, wL4/384EI. 18. Using the method of superposition, determine the slope at A and the deflection at C. EI is constant. Ans. –5PL3/162EI, –PL2/9EI. Using the method of superposition, determine the slope at A and the deflection at C. EI is constant, M = wL2/12. Ans. wL4/384EI, 0.

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