Mechanics of Materials, 7th Edition
7th Edition
ISBN: 9780073398235
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek
Publisher: McGraw-Hill Education
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Chapter 11.5, Problem 50P
(a)
To determine
Find the equivalent static load.
(b)
To determine
Find the maximum stress in the beam
(c)
To determine
The maximum deflection at the midpoint C of the beam.
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Q6 The 2 kg block D is dropped from the position shown onto the end of a 16 mm diameter rod.
Knowing that E = 200 GPa, determine (a) the maximum deflection of end A, (b) the maximum
bending moment in the rod, and (c) the maximum normal stress in the rod.
[Ans. 23.6 mm; 63.38 Nm; 157.6 MPa]
40 mm
D
2 kg
A
0.6 m
B
ΟΙ ΟΙΟΙ
0.6 m
C
Suggestion: use energy methods (Week 5) to find static deflection
The rod ABC is made of an aluminum for which E = 71.4 GPa. Knowing that P = 7.94 kNand Q = 49.88 kN,determine the deflection (in μm) of point B if y = 0.47 and z = 0.54. Round off the final answer in four decimal places.
The length of 2 mm diameter steel wire CD has been adjustedso that with no load is applied, a gap of 1.5 mm exists between the end B ofthe rigid beam ACB and a contact point E. Knowing that E = 200 GPa,determine where a 20 kg block should be placed on the beam in order tocause contact between B and E.
Chapter 11 Solutions
Mechanics of Materials, 7th Edition
Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - The stress-strain diagram shown has been drawn...Ch. 11.3 - The stress-strain diagram shown has been drawn...Ch. 11.3 - Prob. 7PCh. 11.3 - Prob. 8PCh. 11.3 - Using E = 29 106 psi, determine (a) the strain...Ch. 11.3 - Using E = 200 GPa, determine (a) the strain energy...
Ch. 11.3 - A 30-in. length of aluminum pipe of...Ch. 11.3 - A single 6-mm-diameter steel pin B is used to...Ch. 11.3 - Prob. 13PCh. 11.3 - Prob. 14PCh. 11.3 - The assembly ABC is made of a steel for which E =...Ch. 11.3 - Show by integration that the strain energy of the...Ch. 11.3 - Prob. 17PCh. 11.3 - Prob. 18PCh. 11.3 - Prob. 19PCh. 11.3 - 11.18 through 11.21 In the truss shown, all...Ch. 11.3 - Prob. 21PCh. 11.3 - Each member of the truss shown is made of aluminum...Ch. 11.3 - Each member of the truss shown is made of aluminum...Ch. 11.3 - 11.24 through 11.27 Taking into account only the...Ch. 11.3 - Prob. 25PCh. 11.3 - 11.24 through 11.27 Taking into account only the...Ch. 11.3 - 11.24 through 11.27 Taking into account only the...Ch. 11.3 - Prob. 28PCh. 11.3 - Prob. 29PCh. 11.3 - Prob. 30PCh. 11.3 - 11.30 and 11.31 Using E = 200 GPa, determine the...Ch. 11.3 - Assuming that the prismatic beam AB has a...Ch. 11.3 - Prob. 33PCh. 11.3 - The design specifications for the steel shaft AB...Ch. 11.3 - Show by integration that the strain energy in the...Ch. 11.3 - The state of stress shown occurs in a machine...Ch. 11.3 - Prob. 37PCh. 11.3 - The state of stress shown occurs in a machine...Ch. 11.3 - Prob. 39PCh. 11.3 - Prob. 40PCh. 11.3 - Prob. 41PCh. 11.5 - A 5-kg collar D moves along the uniform rod AB and...Ch. 11.5 - The 18-lb cylindrical block E has a horizontal...Ch. 11.5 - The cylindrical block E has a speed v0 =16 ft/s...Ch. 11.5 - Prob. 45PCh. 11.5 - Prob. 46PCh. 11.5 - The 48-kg collar G is released from rest in the...Ch. 11.5 - Prob. 48PCh. 11.5 - Prob. 49PCh. 11.5 - Prob. 50PCh. 11.5 - Prob. 51PCh. 11.5 - The 2-kg block D is dropped from the position...Ch. 11.5 - The 10-kg block D is dropped from a height h = 450...Ch. 11.5 - Prob. 54PCh. 11.5 - A 160-lb diver jumps from a height of 20 in. onto...Ch. 11.5 - Prob. 56PCh. 11.5 - A block of weight W is dropped from a height h...Ch. 11.5 - 11.58 and 11.59 Using the method of work and...Ch. 11.5 - 11.58 and 11.59 Using the method of work and...Ch. 11.5 - 11.60 and 11.61 Using the method of work and...Ch. 11.5 - 11.60 and 11.61 Using the method of work and...Ch. 11.5 - 11.62 and 11.63 Using the method of work and...Ch. 11.5 - 11.62 and 11.63 Using the method of work and...Ch. 11.5 - Using the method of work and energy, determine the...Ch. 11.5 - Using the method of work and energy, determine the...Ch. 11.5 - The 20-mm diameter steel rod BC is attached to the...Ch. 11.5 - Torques of the same magnitude T are applied to the...Ch. 11.5 - Prob. 68PCh. 11.5 - The 20-mm-diameter steel rod CD is welded to the...Ch. 11.5 - The thin-walled hollow cylindrical member AB has a...Ch. 11.5 - 11.71 and 11.72 Each member of the truss shown has...Ch. 11.5 - 11.71 and 11.72 Each member of the truss shown has...Ch. 11.5 - Each member of the truss shown is made of steel...Ch. 11.5 - Each member of the truss shown is made of steel....Ch. 11.5 - Each member of the truss shown is made of steel...Ch. 11.5 - The steel rod BC has a 24-mm diameter and the...Ch. 11.9 - 11.77 and 11.78 Using the information in Appendix...Ch. 11.9 - 11.77 and 11.78 Using the information in Appendix...Ch. 11.9 - 11.79 through 11.82 For the beam and loading...Ch. 11.9 - 11.79 through 11.82 For the beam and loading...Ch. 11.9 - 11.79 through 11.82 For the beam and loading...Ch. 11.9 - 11.79 through 11.82 For the beam and loading...Ch. 11.9 - 11.83 through 11.85 For the prismatic beam shown,...Ch. 11.9 - 11.83 through 11.85 For the prismatic beam shown,...Ch. 11.9 - 11.83 through 11.85 For the prismatic beam shown,...Ch. 11.9 - 11.86 through 11.88 For the prismatic beam shown,...Ch. 11.9 - 11.86 through 11.88 For the prismatic beam shown,...Ch. 11.9 - 11.86 through 11.88 For the prismatic beam shown,...Ch. 11.9 - For the prismatic beam shown, determine the slope...Ch. 11.9 - For the prismatic beam shown, determine the slope...Ch. 11.9 - For the beam and loading shown, determine the...Ch. 11.9 - For the beam and loading shown, determine the...Ch. 11.9 - 11.93 and 11.94 For the beam and loading shown,...Ch. 11.9 - 11.93 and 11.94 For the beam and loading shown,...Ch. 11.9 - For the beam and loading shown, determine the...Ch. 11.9 - For the beam and loading shown, determine the...Ch. 11.9 - Prob. 97PCh. 11.9 - For the beam and loading shown, determine the...Ch. 11.9 - 11.99 and 11.100 For the truss and loading shown,...Ch. 11.9 - 11.99 and 11.100 For the truss and loading shown,...Ch. 11.9 - 11.101 and 11.102 Each member of the truss shown...Ch. 11.9 - 11.101 and 11.102 Each member of the truss shown...Ch. 11.9 - 11.103 and 11.104 Each member of the truss shown...Ch. 11.9 - 11.103 and 11 104 Each member of the truss shown...Ch. 11.9 - A uniform rod of flexural rigidity EI is bent and...Ch. 11.9 - For the uniform rod and loading shown and using...Ch. 11.9 - For the beam and loading shown and using...Ch. 11.9 - Two rods AB and BC of the same flexural rigidity...Ch. 11.9 - Three rods, each of the same flexural rigidity EI,...Ch. 11.9 - Three rods, each of the same flexural rigidity EI,...Ch. 11.9 - 11.111 through 11.115 Determine the reaction at...Ch. 11.9 - 11.111 through 11.115 Determine the reaction at...Ch. 11.9 - 11.111 through 11.115 Determine the reaction at...Ch. 11.9 - 11.111 through 11.115 Determine the reaction at...Ch. 11.9 - 11.111 through 11.115 Determine the reaction at...Ch. 11.9 - For the uniform beam and loading shown, determine...Ch. 11.9 - 11.117 through 11.120 Three members of the same...Ch. 11.9 - 11.117 through 11.120 Three members of the same...Ch. 11.9 - 11.117 through 11.120 Three members of the same...Ch. 11.9 - 11.117 through 11.120 Three members of the same...Ch. 11.9 - 11.121 and 11.122 Knowing that the eight members...Ch. 11.9 - 11.121 and 11.122 Knowing that the eight members...Ch. 11 - Rod AB is made of a steel for which the yield...Ch. 11 - Each member of the truss shown is made of steel...Ch. 11 - The ship at A has just started to drill for oil on...Ch. 11 - Collar D is released from rest in the position...Ch. 11 - Each member of the truss shown is made of steel...Ch. 11 - A block of weight W is placed in contact with a...Ch. 11 - Two solid steel shafts are connected by the gears...Ch. 11 - A 160-lb diver jumps from a height of 20 in. onto...Ch. 11 - For the prismatic beam shown, determine the slope...Ch. 11 - A disk of radius a has been welded to end B of the...Ch. 11 - A uniform rod of flexural rigidity EI is bent and...Ch. 11 - The steel bar ABC has a square cross section of...
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- A 5-m-long, simply supported steel beam AD is to carry the distributed and concentrated loads shown. Knowing that the allowable normal stress for the grade of steel is 160 MPa, select the wide-flange shape to be used.arrow_forward11.9 (A/B). Develop from first principles an expression for the instantaneous stress set up in a vertical bar by a weight W falling from a height h on to a stop at the end of the bar. The instantaneous extension x may not be neglected. A weight of 500 N can slide freely on a vertical steel rod 2.5 m long and 20 mm diameter. The rod is rigidly fixed at its upper end and has a collar at the lower end to prevent the weight from dropping off. The weight is lifted to a distance of 50 mm above the collar and then released. Find the maximum instantaneous stress produced in the rod. E = 200 GN/m³. [114 MN/m²]arrow_forwardShow all the work, don't use gpt.arrow_forward
- The length of the 2-mm diameter steel wire CD has been adjusted so that with no load applied, a gap of 1.5mm exists between the end B of the rigid beam ACB and a contact point E. knowing that E = 200 GPa, determine where a 20-kg block should be placed on the beam in order to cause contact between B and E. D 0.23 m 20 kg B с 0.08 m 0.32 marrow_forwardBoth portions of the rod ABC are made out of an aluminum forwhich E = 70 GPa. Knowing that the magnitude of P is 4 kN, determine (a)the value of Q so that the deflection at A is zero, (b) the correspondingdeflection of B.arrow_forwardBefore the uniformly distributed load w is applied, a gap, 80 = 1.2 mm, exists between the ends of the cantilever bars AB and CD. Knowing that E = 105 GPa and w = 30 kN/m, determine the reaction (a) at A, (b) at D. ბი 50 mm 400 mm 250 mm D 50 mm (a) 10.86 kN ; 1.942 kN·m →. (b) 1.144 kN ↑; 0.286 kN·m .arrow_forward
- w=15arrow_forward5.arrow_forwardA load P is supported as shown by a steel pin that has been inserted in a short wooden member hanging from the ceiling. The ultimate strength of the wood used is 60 MPa in tension and 7.5 MPa in shear,while the ultimate strength of the steel is 145 MPa in shear. Knowing that b = 40 mm, c = 55 mm, and d = 12 mm, determine the load P if an overall factor of safety of 3.2 is desired.arrow_forward
- 1418. A weight is dropped from a position just above, but not touching, a spring. Show that the maximum deformation produced will be twice that if the same weight is gradually lowered upon the spring. Answer: 15.3 ft per secarrow_forwardFbd ,formula and calculation should be included. Please work it fast without wasting a time. 1)The rod ABC is made of an aluminum for which E = 70 GPa. Knowing that P = 9 kN and Q = 14 kN, determine the deflection of: (a) Point A, (b) Point B. Consider upward to be positive.arrow_forwardPROBLEM 10.21 10.21 The uniform brass bar AB has a rectangular cross section and is supported by pins and brackets as shown. Each end of the bar can rotate freely about a horizontal axis through the pin, but rotation about a vertical axis is prevented by the brackets. (a) Determine the ratio bld for which the factor of safety is the same about the horizontal and vertical axes. (b) Determine the factor of safety if P = 8 L = 2m, d = 38 mm, and E = 105 GPa. B kN,arrow_forward
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