EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 8220100257063
Author: BEER
Publisher: YUZU
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Chapter 6.6, Problem 82P
To determine
The distribution of the shearing stresses along line
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5.86 The cast iron inverted T-section supports two concentrated loads of magnitude P. The working stresses are 48 MPa in tension, 140 MPa in compression, and 30 MPa in shear. (a) Show that the neutral axis of the cross section is located at d ¼ 48:75 mm and that the moment of inertia of the cross-sectional area about this axis is I ¼ 11:918 106 mm4. (b) Find the maximum allowable value of P.
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A 1600-lb-in. couple is applied to a wooden beam, of rectangular cross section 1.5 by 3.5 in., in a plane forming an angle of 308 with the vertical (Fig. ). Determine (a) the maximum stress in the beam and (b) the angle that the neutral surface forms with the horizontal plane
Chapter 6 Solutions
EBK MECHANICS OF MATERIALS
Ch. 6.2 - Three full-size 50 100-mm boards are nailed...Ch. 6.2 - For the built-up beam of Prob. 6.1, determine the...Ch. 6.2 - Three boards, each 2 in. thick, are nailed...Ch. 6.2 - A square box beam is made of two 20 80-mm planks...Ch. 6.2 - The American Standard rolled-steel beam shown has...Ch. 6.2 - The beam shown is fabricated by connecting two...Ch. 6.2 - A column is fabricated by connecting the...Ch. 6.2 - The composite beam shown is fabricated by...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...
Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.9 through 6.12 For beam and loading shown,...Ch. 6.2 - 6.13 and 6.14 For a beam having the cross section...Ch. 6.2 - 6.13 and 6.14 For a beam having the cross section...Ch. 6.2 - For a timber beam having the cross section shown,...Ch. 6.2 - Two steel plates of 12 220-mm rectangular cross...Ch. 6.2 - Two W8 31 rolled sections may be welded at A and...Ch. 6.2 - For the beam and. loading shown, determine the...Ch. 6.2 - Fig. P6.19 6.19 A timber beam AB of length L and...Ch. 6.2 - A timber beam AB of Length L and rectangular cross...Ch. 6.2 - 6.21 and 6.22 For the beam and loading shown,...Ch. 6.2 - 6.21 and 6.22 For the beam and loading shown,...Ch. 6.2 - 6.23 and 6.24 For the beam and loading shown,...Ch. 6.2 - 6.23 and 6.24 For the beam and loading shown,...Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.2 - Prob. 27PCh. 6.2 - 6.25 through 6.28 A beam having the cross section...Ch. 6.5 - The built-up timber beam shown is subjected to a...Ch. 6.5 - The built-up beam shown is made by gluing together...Ch. 6.5 - The built-up beam was made by gluing together...Ch. 6.5 - Several wooden planks are glued together to form...Ch. 6.5 - The built-up wooden beam shown is subjected to a...Ch. 6.5 - Knowing that a W360 122 rolled-steel beam is...Ch. 6.5 - 6.35 and 6.36 An extruded aluminum beam has the...Ch. 6.5 - 6.35 and 6.36 An extruded aluminum beam has the...Ch. 6.5 - Knowing that a given vertical shear V causes a...Ch. 6.5 - The vertical shear is 1200 lb in a beam having the...Ch. 6.5 - The vertical shear is 1200 lb in a beam having the...Ch. 6.5 - 6.40 and 6.47 The extruded aluminum beam has a...Ch. 6.5 - Prob. 41PCh. 6.5 - Prob. 42PCh. 6.5 - Three planks are connected as shown by bolts of...Ch. 6.5 - A beam consists of three planks connected as shown...Ch. 6.5 - A beam consists of five planks of 1.5 6-in. cross...Ch. 6.5 - Four L102 102 9.5 steel angle shapes and a 12 ...Ch. 6.5 - A plate of 14-in. thickness is corrugated as shown...Ch. 6.5 - Prob. 48PCh. 6.5 - An extruded beam has the cross section shown and a...Ch. 6.5 - Prob. 50PCh. 6.5 - The design of a beam calls for connecting two...Ch. 6.5 - The cross section of an extruded beam is a hollow...Ch. 6.5 - Prob. 53PCh. 6.5 - Prob. 54PCh. 6.5 - Prob. 55PCh. 6.5 - 6.56 and 6.57 A composite beam is made by...Ch. 6.5 - 6.56 and 6.57 A composite beam is made by...Ch. 6.5 - Prob. 58PCh. 6.5 - Prob. 59PCh. 6.5 - Prob. 60PCh. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - 6.61 through 6.64 Determine the location of the...Ch. 6.6 - Prob. 64PCh. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.65 through 6.68 An extruded beam has the cross...Ch. 6.6 - 6.69 through 6.74 Determine the location of the...Ch. 6.6 - Prob. 70PCh. 6.6 - Prob. 71PCh. 6.6 - Prob. 72PCh. 6.6 - Prob. 73PCh. 6.6 - Prob. 74PCh. 6.6 - Prob. 75PCh. 6.6 - 6.75 and 6.76 A thin-walled beam has the cross...Ch. 6.6 - 6.77 and 6.78 A thin-walled beam of uniform...Ch. 6.6 - Prob. 78PCh. 6.6 - Prob. 79PCh. 6.6 - Prob. 80PCh. 6.6 - Prob. 81PCh. 6.6 - Prob. 82PCh. 6.6 - Prob. 83PCh. 6.6 - Prob. 84PCh. 6.6 - Prob. 85PCh. 6.6 - Solve Prob. 6.85, assuming that the thickness of...Ch. 6.6 - Prob. 87PCh. 6.6 - Prob. 88PCh. 6 - Three boards are nailed together to form the beam...Ch. 6 - For the beam and loading shown, consider section...Ch. 6 - For the wide-flange beam with the loading shown,...Ch. 6 - For the beam and loading shown, consider section...Ch. 6 - The built-up timber beam is subjected to a 1500-lb...Ch. 6 - Knowing that a given vertical shear V causes a...Ch. 6 - Three planks are connected as shown by bolts of...Ch. 6 - Three 1 18-in. steel plates are bolted to four L6...Ch. 6 - The composite beam shown is made by welding C200 ...Ch. 6 - Prob. 98RPCh. 6 - A thin-walled beam of uniform thickness has the...Ch. 6 - Determine the location of the shear center O of a...
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- PROBLEM 7.26 0.2 m The axle of an automobile is acted upon by the forces and couple shown. Knowing that the diameter of the solid axle is 32 mm, determine (a) the principal planes and principal stresses at point H located on top of the axle, (b) the maximum shearing stress at the same point. 3 kN 350 N- m 3 kN Omax = 18.67 MPa = -158,5 MPa O minarrow_forwardI need the solution for this problem. Under normal operating conditions, the electric motor exerts a torque at point E of 12 kip-in. Knowing that each axis is solid, determine the maximum shear stress on (a) axis BC, (b) axis CD, (c) axis DE.arrow_forwardQue 5.6. A crane hook trapezoidal horizontal cross-section is 50 mm wide inside and 30 mm wide outside. Thickness of the section is 60 mm. The crane hook carries a vertical load of 20 kN whose line of action is 50 mm from the inside edge of the section. The center of curvature is 60 mm from the inside edge. Determine the maximum tensile and compressive stresses in the section.arrow_forward
- The two forces shown are applied to a rigid plate supported by a steel pipe of 8-in. outer diameter and 7-in. inner diameter. Determine the value of P for which the maximum compressive stress in the pipe is 15 ksiarrow_forwardP.16.4 A thin-walled cantilever with walls of constant thickness t has the cross- section shown in Fig. P.16.4. It is loaded by a vertical force W at the tip and a horizontal force 2W at the mid-section, both forces acting through the shear centre. Determine and sketch the distribution of direct stress, according to the basic theory of bending, along the length of the beam for the points 1 and 2 of the cross-section. The wall thickness t can be taken as very small in comparison with d in calculating the sectional properties Lxx, Ixy, etc. Ans. 2,1 (mid-point) = -0.05 Wl/td², 02,1 (built-in end) = -1.85 Wl/td² ₂2 (mid-point) = -0.63 W1/td², 02 (built-in end) = 0.1 Wl/td². /////// Fig. P.16.4 W 7/2 2W 1/2 A 2 d12_ _d12. 3 Xarrow_forwardShow all workarrow_forward
- 2. Link AB, of width b 5 50 mm and thickness t 5 6 mm, is used to support the end of a horizontal beam. Knowing that the average normal stress in the link is 2140 MPa, and that the average shearing stress in each of the two pins is 80 MPa, determine (a) the diameter d of the pins, (b) the average bearing stress in the link.arrow_forward1.4 kN - m PROBLEM 8.43 A 10-kN force and a 1.4-kN - m couple are applied at the top of the 65-mm diameter brass post shown. Determine the principal stresses and maximum shearing stress at (a) point H, (b) point K. 10 kN 240 mm Omax = 30.0 MPa O min =-30.0 MPa Tmax = 30.0 MPa Omax = 7.02 MPa Omin =-96.0 MPa Tmay =51.5 MPaarrow_forwardA timber beam AB of length L and rectangular cross section carries a single concentrated load P at its midpoint C. (a) Show that the ratio Tm/ m of the maximum values of the shearing and normal stresses in the beam is equal to h/2L, where h and L are, respectively, the depth and the length of the beam. (b) Determine the depth h and the width b of the beam, knowing that L = 2 m, P = 40 kN, 7m = 960 kPa, and om = 12 MPa.arrow_forward
- L/4 D L/2 LA B A timber beam AB of length L and rectangular cross section carries a uniformly distributed load w and is supported as shown. (a) Show that the ratio of the maximum values of the shearing and normal stresses in the beam is equal to 2h/L, where h and L are, respectively, the depth and the length of the beam. (b) Determine the depth h and the width b of the beam, knowing that L = 5 m, w = 8 kN/m, Tm = 1.08 MPa, and om = 12 MPa.arrow_forward5.82 The simply supported wood beam, fabricated by gluing together fourwooden boards, carries the three concentrated forces. The working bending and shear stresses for the wood are 1000 psi and 600 psi, respectively. Determine the largest allowable value of the force P.arrow_forward3.5 A torque T = 3 kN • m is applied to the solid bronze cylinder shown. Determine (a) the maximum shearing stress, (b) the shear- ing stress at point D, which lies on a 15-mm-radius circle drawn on the end of the cylinder, (e) the percent of the torque carried by the portion of the cylinder within the l15-mm radius. 60 mm 30 mm T=3 kN- m - 200 min Fig. P3.5arrow_forward
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