MECHANICAL ENGINEERING DES.(LL)-W/CNCT
15th Edition
ISBN: 9781260531374
Author: BUDYNAS
Publisher: MCG
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Textbook Question
Chapter 3, Problem 46P
Consider a simply supported beam of rectangular cross section of constant width b and variable depth h. so proportioned that the maximum stress σx at the outer surface due to bending is constant, when subjected to a load F at a distance a from the left support and a distance c from the right support. Show that the depth h at location x is given by
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Chapter 3 Solutions
MECHANICAL ENGINEERING DES.(LL)-W/CNCT
Ch. 3 - 31 to 34 Sketch a free-body diagram of each...Ch. 3 - 31 to 34 Sketch a free-body diagram of each...Ch. 3 - Sketch a free-body diagram of each element in the...Ch. 3 - 3-1 to 3-4 Sketch a free-body diagram of each...Ch. 3 - 35 to 38 For the beam shown, find the reactions at...Ch. 3 - 35 to 38 For the beam shown, find the reactions at...Ch. 3 - 35 to 38 For the beam shown, find the reactions at...Ch. 3 - For the beam shown, find the reactions at the...Ch. 3 - For the beam shown, find the reactions at the...Ch. 3 - Repeat Prob. 36 using singularity functions...
Ch. 3 - Repeat Prob. 37 using singularity functions...Ch. 3 - Repeat Prob. 38 using singularity functions...Ch. 3 - For a beam from Table A9, as specified by your...Ch. 3 - A beam carrying a uniform load is simply supported...Ch. 3 - For each of the plane stress states listed below,...Ch. 3 - Repeat Prob. 315 for: (a)x = 28 MPa, y = 7 MPa, xy...Ch. 3 - Repeat Prob. 315 for: a) x = 12 kpsi, y = 6 kpsi,...Ch. 3 - For each of the stress states listed below, find...Ch. 3 - Repeat Prob. 318 for: (a)x = 10 kpsi, y = 4 kpsi...Ch. 3 - The state of stress at a point is x = 6, y = 18, z...Ch. 3 - The state of stress at a point is x = 6, y = 18, z...Ch. 3 - Repeat Prob. 320 with x = 10, y = 40, z = 40, xy =...Ch. 3 - A 34-in-diameter steel tension rod is 5 ft long...Ch. 3 - Repeat Prob. 323 except change the rod to aluminum...Ch. 3 - A 30-mm-diameter copper rod is 1 m long with a...Ch. 3 - A diagonal aluminum alloy tension rod of diameter...Ch. 3 - Repeat Prob. 326 with d = 16 mm, l = 3 m, and...Ch. 3 - Repeat Prob. 326 with d = 58 in, l = 10 ft, and...Ch. 3 - Electrical strain gauges were applied to a notched...Ch. 3 - Repeat Prob. 329 for a material of aluminum. 3-29...Ch. 3 - The Roman method for addressing uncertainty in...Ch. 3 - Using our experience with concentrated loading on...Ch. 3 - The Chicago North Shore Milwaukee Railroad was an...Ch. 3 - For each section illustrated, find the second...Ch. 3 - 3-35 to 3-38 For the beam illustrated in the...Ch. 3 - 3-35 to 3-38 For the beam illustrated in the...Ch. 3 - 3-35 to 3-38 For the beam illustrated in the...Ch. 3 - 3-35 to 3-38 For the beam illustrated in the...Ch. 3 - The figure illustrates a number of beam sections....Ch. 3 - A pin in a knuckle joint canning a tensile load F...Ch. 3 - Repeat Prob. 3-40 for a = 6 mm, b = 18 mm. d = 12...Ch. 3 - For the knuckle joint described in Prob. 3-40,...Ch. 3 - The figure illustrates a pin tightly fitted into a...Ch. 3 - For the beam shown, determine (a) the maximum...Ch. 3 - A cantilever beam with a 1-in-diameter round cross...Ch. 3 - Consider a simply supported beam of rectangular...Ch. 3 - In Prob. 346, h 0 as x 0, which cannot occur. If...Ch. 3 - 348 and 349 The beam shown is loaded in the xy and...Ch. 3 - The beam shown is loaded in the xy and xz planes....Ch. 3 - Two steel thin-wall tubes in torsion of equal...Ch. 3 - Consider a 1-in-square steel thin-walled tube...Ch. 3 - The thin-walled open cross-section shown is...Ch. 3 - 3-53 to 3-55 Using the results from Prob. 3-52,...Ch. 3 - 3-53 to 3-55 Using the results from Prob. 3-52,...Ch. 3 - 3-53 to 3-55 Using the results from Prob. 3-52,...Ch. 3 - Two 300-mm-long rectangular steel strips are...Ch. 3 - Using a maximum allowable shear stress of 70 Mpa,...Ch. 3 - Repeat Prob. 357 with an allowable shear stress of...Ch. 3 - Using an allowable shear stress of 50 MPa,...Ch. 3 - A 20-mm-diameter steel bar is to be used as a...Ch. 3 - A 2-ft-long steel bar with a 34-in diameter is to...Ch. 3 - A 40-mm-diameter solid steel shaft, used as a...Ch. 3 - Generalize Prob. 3-62 for a solid shaft of...Ch. 3 - A hollow steel shaft is to transmit 4200 N m of...Ch. 3 - The figure shows an endless-bell conveyor drive...Ch. 3 - The conveyer drive roll in the figure for Prob....Ch. 3 - Consider two shafts in torsion, each of the same...Ch. 3 - 3-68 to 3-71 A countershaft two V-belt pulleys is...Ch. 3 - 3-68 to 3-71 A countershaft two V-belt pulleys is...Ch. 3 - 3-68 to 3-71 A countershaft two V-belt pulleys is...Ch. 3 - A countershaft carrying two V-belt pulleys is...Ch. 3 - A gear reduction unit uses the countershaft shown...Ch. 3 - Prob. 73PCh. 3 - Prob. 74PCh. 3 - Prob. 75PCh. 3 - Prob. 76PCh. 3 - Prob. 77PCh. 3 - Prob. 78PCh. 3 - Prob. 79PCh. 3 - The cantilevered bar in the figure is made from a...Ch. 3 - Repeat Prob. 3-80 with Fx = 0, Fy = 175 lbf, and...Ch. 3 - Repeat Prob. 3-80 with Fx = 75 lbf, Fy= 200 lbf,...Ch. 3 - For the handle in Prob. 3-80, one potential...Ch. 3 - The cantilevered bar in the figure is made from a...Ch. 3 - Repeat Prob. 3-84 with Fx = 300 lbf, Fy = 250 lbf,...Ch. 3 - Repeat Prob. 3-84 with Fx = 300 lbf, Fy = 250 lbf,...Ch. 3 - Repeat Prob. 3-84 for a brittle material,...Ch. 3 - Repeat Prob. 3-84 with Fx = 300 lbf, Fy = 250 lbf,...Ch. 3 - Repeat Prob. 3-84 with Fx = 300 lbf, Fy = 250 lbf,...Ch. 3 - The figure shows a simple model of the loading of...Ch. 3 - Develop the formulas for the maximum radial and...Ch. 3 - Repeat Prob. 391 where the cylinder is subject to...Ch. 3 - Develop the equations for the principal stresses...Ch. 3 - 3-94 to 3-96 A pressure cylinder has an outer...Ch. 3 - 3-94 to 3-96 A pressure cylinder has an outer...Ch. 3 - 3-94 to 3-96A pressure cylinder has an outer...Ch. 3 - 3-97 to 3-99 A pressure cylinder has an outer...Ch. 3 - 3-97 to 3-99 A pressure cylinder has an outer...Ch. 3 - 3-97 to 3-99 A pressure cylinder has an outer...Ch. 3 - An AISI 1040 cold-drawn steel tube has an OD = 50...Ch. 3 - Repeat Prob. 3-100 with an OD of 2 in and wall...Ch. 3 - Prob. 102PCh. 3 - Prob. 103PCh. 3 - A thin-walled cylindrical Steel water storage tank...Ch. 3 - Repeat Prob. 3-104 with the tank being pressurized...Ch. 3 - Find the maximum shear stress in a 512-in-diameter...Ch. 3 - The maximum recommended speed for a...Ch. 3 - An abrasive cutoff wheel has a diameter of 5 in,...Ch. 3 - A rotary lawnmower blade rotates at 3500 rev/min....Ch. 3 - 3110 to 3115 The table lists the maximum and...Ch. 3 - Prob. 111PCh. 3 - Prob. 112PCh. 3 - 3110 to 3115 The table lists the maximum and...Ch. 3 - Prob. 114PCh. 3 - Prob. 115PCh. 3 - 3116 to 3119 The table gives data concerning the...Ch. 3 - Prob. 117PCh. 3 - Prob. 118PCh. 3 - 3116 to 3119 The table gives data concerning the...Ch. 3 - A utility hook was formed from a round rod of...Ch. 3 - A utility hook was formed from a round rod of...Ch. 3 - The steel eyebolt shown in the figure is loaded...Ch. 3 - For Prob. 3122 estimate the stresses at the inner...Ch. 3 - Repeat Prob. 3122 with d = 14 in, Ri = 12 in, and...Ch. 3 - Repeat Prob. 3123 with d = 14 in, Ri = 12 in, and...Ch. 3 - Shown in the figure is a 12-gauge (0.1094-in) by...Ch. 3 - Repeat Prob. 3126 with a 10-gauge (0.1406-in)...Ch. 3 - Prob. 128PCh. 3 - The cast-iron bell-crank lever depicted in the...Ch. 3 - Prob. 130PCh. 3 - Prob. 131PCh. 3 - A cast-steel C frame as shown in the figure has a...Ch. 3 - Two carbon steel balls, each 30 mm in diameter,...Ch. 3 - A carbon steel ball with 25-mm diameter is pressed...Ch. 3 - Repeat Prob. 3134 but determine the maximum shear...Ch. 3 - A carbon steel ball with a 30-mm diameter is...Ch. 3 - An AISI 1018 steel ball with 1-in diameter is used...Ch. 3 - An aluminum alloy cylindrical roller with diameter...Ch. 3 - A pair of mating steel spur gears with a 0.75-in...Ch. 3 - 3140 to 3142 A wheel of diameter d and width w...Ch. 3 - 3140 to 3142 A wheel of diameter d and width w...Ch. 3 - 3140 to 3142 A wheel of diameter d and width w...
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- The beam is made of four aluminium plates welded together as shown in Figure 1. Knowing that E = 65 GPa and neglecting the effect of the fillet. i. An engineer has been asked to change the material of the beam from aluminium to bronze, having ultimate normal stress 600 MPa, and E = 100 GPa. The design of the beam will remain as per Figure 1. Determine the maximum bending moment M that can be applied from which the factor of safety will be 2.5.arrow_forwardSuppose that w1 = 15 kN/m and w2 = 7.5 kN/m. Specify the location of FR on the beam, measured from point B to the right.arrow_forwardThe neutral axis of the cross-section a beam is that axis at which the bending stress is A. zero B. minimum C. maximum D. infinityarrow_forward
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- If the beam has a rectangular cross-section, then the shear-stress distribution will be parabolic. True or False?arrow_forwardA cantilever beam of length 6 m carries a uniformly distributed load of 2.5 kN/m over its entire length. Determine the maximum deflection and slope if E = 210 GPa and I = 12.5 x 106 mm4.arrow_forward1–1. The shaft is supported by a smooth thrust bearing at B and a journal bearing at C. Determine the resultant internal loadings acting on the cross section at E. Problem 1–1arrow_forward
- A beam has the singly symmetrical thin-walled cross section shown in the figure. The thickness t of the wall is constant throughout. Show that the distance of the shear center from the web is given by d pzsinrxcosa Sy = md ey 14+6p+2p°sin“a where p=d/harrow_forwardDetermine the shear force acting at each of the following locations:(a) x = 0+ ft (i.e., just to the right of support A)(b) x = 9 ft(c) x = 12.333333333333 ftWhen entering your answers, use the shear force sign convention.Answer:(a) V = kips.(b) V = kips.(c) V = kips. The shear-force diagram crosses the V = 0 axis between points A and B. Determine the location x where V = 0 kips.Answer: x = Enter your answer in accordance to the question statement ft. Determine the maximum bending moment that acts anywhere in the beam. When entering your answer, use the bending moment sign convention.Answer: Mmax = Enter your answer in accordance to the question statement kip-ft. Use the graphical method to determine the bending moment acting at each of the following locations:(a) x = 3.3 ft(b) x = 9 ft(c) x = 12.6 ftWhen entering your answers, use the bending moment sign convention.Answers:(a) M = kip-ft.(b) M = kip-ft.(c) M = kip-ft.arrow_forwardIf the allowable tensile and compressive stress for the beam are (sallow)t = 2 ksi and (sallow)c = 3 ksi, respectively, determine the maximum moment M that can be applied on the cross section.arrow_forward
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