EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 8220100257063
Author: BEER
Publisher: YUZU
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Textbook Question
Chapter 9.4, Problem 80P
Use the method of superposition to solve the following problems and assume that the flexural rigidity El of each beam is constant.
9.79 and 9.80 For the uniform beam shown, determine (a) the reaction at A, (b) the reaction at B.
Fig. P9.80
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An overhang beam with negligible weight is loaded as shown.
Knowing that the flexural rigidity of the beam is El = 2 × 105 kNm², (a) Reactions at A and B
(a) determine the reactions at supports A and B, (b) derive the elastic (b) section AB
curve for section AB, (c) derive the elastic curve for section BC, and v =
(d) determine the deflection at point C.
v =
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v =
(d)
m
m
Problem 2. (a) Draw the moment diagram for the
beam. (b) Observing the direction of load and sign of
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beam section, (c) Using integration, determine the
equation of the elastic curve for the beam using the x
coordinate that is valid for 0 < x < L/2. (d) Specify the
slope at A and the beam's maximum deflection. El is
constant. For parts (a) and (b), model only one-half of
the beam, from x=0 to x=L/2, and use the symmetry
dv
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of symmetry at x=L/2.
dx
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B
Determine the maximum deflection for the beams shown in Figs. P6.23 through P6.30 by the conjugate-beam method.
Chapter 9 Solutions
EBK MECHANICS OF MATERIALS
Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - 9.1 through 9.4 For the loading shown, determine...Ch. 9.2 - 9.5 and 9.6 For the cantilever beam and loading...Ch. 9.2 - 9.5 and 9.6 For the cantilever beam and loading...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - Knowing that beam .AB is a W10 33 rolled shape...Ch. 9.2 - Knowing that beam AB is an S200 34 roiled shape...
Ch. 9.2 - For the beam and loading shown, (a) express the...Ch. 9.2 - (a) Determine the location and magnitude of the...Ch. 9.2 - For the beam and loading shown, determine the...Ch. 9.2 - Knowing that beam AE is a W360 101 rolled shape...Ch. 9.2 - For the beam and loading shown, knowing that a = 2...Ch. 9.2 - Knowing that beam AE is an S200 27.4 rolled shape...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - 9.19 through 9.22 For the beam and loading shown,...Ch. 9.2 - 9.19 through 9.22 For the beam and loading shown,...Ch. 9.2 - 9.19 through 9.22 For the beam and loading shown,...Ch. 9.2 - 9.19 through 9.22 For the beam and loading shown,...Ch. 9.2 - For the beam shown, determine the reaction at the...Ch. 9.2 - For the beam shown, determine the reaction at the...Ch. 9.2 - 9.25 through 9.28 Determine the reaction at the...Ch. 9.2 - 9.25 through 9.28 Determine the reaction at the...Ch. 9.2 - Prob. 27PCh. 9.2 - 9.25 through 9.28 Determine the reaction at the...Ch. 9.2 - 9.29 and 9.30 Determine the reaction at the roller...Ch. 9.2 - 9.29 and 9.30 Determine the reaction at the roller...Ch. 9.2 - 9.37 and 9.32 Determine the reaction at the roller...Ch. 9.2 - 9.31 and 9.32 Determine the reaction at the roller...Ch. 9.2 - Prob. 33PCh. 9.2 - 9.33 and 9.34 determine the reaction at A and draw...Ch. 9.3 - 9.35 and 9.36 For the beam and loading shown,...Ch. 9.3 - 9.35 and 9.36 For the beam and loading shown,...Ch. 9.3 - 9.37 and 9.38 For the beam and loading shown,...Ch. 9.3 - 9.37 and 9.38 For the beam and loading shown,...Ch. 9.3 - 9.39 and 9.40 For the beam and loading shown,...Ch. 9.3 - 9.39 and 9.40 For the beam and loading shown,...Ch. 9.3 - 9.41 and 9.42 For the beam and loading shown,...Ch. 9.3 - 9.41 and 9.42 For the beam and loading shown (a)...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the timber beam and loading shown, determine...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - 9.49 and 9.50 For the beam and loading shown,...Ch. 9.3 - 9.49 and 9.50 For the beam and loading shown,...Ch. 9.3 - 9.51 and 9.52 For the beam and loading shown,...Ch. 9.3 - 9.49 and 9.50 For the beam and loading shown,...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam shown, and knowing that P = 40 kN,...Ch. 9.3 - 9.55 and 9.56 For the beam and loading shown, (a)...Ch. 9.3 - 9.55 and 9.56 For the beam and loading shown, (a)...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - For the beam and loading shown, determine (a) the...Ch. 9.3 - Prob. 59PCh. 9.3 - 9.59 through 9.62 For the beam and loading...Ch. 9.3 - Prob. 61PCh. 9.3 - 9.59 through 9.62 For the beam and loading...Ch. 9.3 - The rigid bars BF and DH are welded to the...Ch. 9.3 - The rigid bar DEF is welded at point D to the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Prob. 84PCh. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.4 - Use the method of superposition to solve the...Ch. 9.5 - 9.95 through 9.98 For the uniform cantilever beam...Ch. 9.5 - Prob. 96PCh. 9.5 - 9.95 through 9.98 For the uniform cantilever beam...Ch. 9.5 - 9.95 through 9.98 For the uniform cantilever beam...Ch. 9.5 - 9.99 and 9.100 For the uniform cantilever beam and...Ch. 9.5 - 9.99 and 9.100 For the uniform cantilever beam and...Ch. 9.5 - For the cantilever beam and loading shown,...Ch. 9.5 - Prob. 102PCh. 9.5 - Prob. 103PCh. 9.5 - Prob. 104PCh. 9.5 - Prob. 105PCh. 9.5 - For the cantilever beam and loading shown,...Ch. 9.5 - Two cover plates are welded to the rolled-steel...Ch. 9.5 - Two cover plates are welded to the rolled-steel...Ch. 9.5 - 9.109 through 9.114 For the prismatic beam and...Ch. 9.5 - Prob. 110PCh. 9.5 - Prob. 111PCh. 9.5 - Prob. 112PCh. 9.5 - Prob. 113PCh. 9.5 - Prob. 114PCh. 9.5 - Prob. 115PCh. 9.5 - 9.115 and 9.116 For the beam and loading shown,...Ch. 9.5 - Prob. 117PCh. 9.5 - 9.118 and 9.119 For the beam and loading shown,...Ch. 9.5 - Prob. 119PCh. 9.5 - Prob. 120PCh. 9.5 - Prob. 121PCh. 9.5 - Prob. 122PCh. 9.5 - Prob. 123PCh. 9.5 - Prob. 124PCh. 9.6 - 9.125 through 9.128 For the prismatic beam and...Ch. 9.6 - Prob. 126PCh. 9.6 - Prob. 127PCh. 9.6 - Prob. 128PCh. 9.6 - 9.129 and 9.130 For the beam and loading shown,...Ch. 9.6 - Prob. 130PCh. 9.6 - For the timber beam and loading shown, determine...Ch. 9.6 - Prob. 132PCh. 9.6 - For the beam and loading shown, determine (a) the...Ch. 9.6 - Prob. 134PCh. 9.6 - Prob. 135PCh. 9.6 - Knowing that the beam AD is made of a solid steel...Ch. 9.6 - Prob. 137PCh. 9.6 - For the beam and loading shown, determine (a) the...Ch. 9.6 - Prob. 139PCh. 9.6 - For the beam and loading shown, determine the...Ch. 9.6 - Prob. 141PCh. 9.6 - Prob. 142PCh. 9.6 - Prob. 143PCh. 9.6 - Prob. 144PCh. 9.6 - Prob. 145PCh. 9.6 - For the beam and loading shown, determine (a) the...Ch. 9.6 - Prob. 147PCh. 9.6 - Prob. 148PCh. 9.6 - Prob. 149PCh. 9.6 - Prob. 150PCh. 9.6 - 9.151 and 9.152 For the beam and loading shown,...Ch. 9.6 - Prob. 152PCh. 9.6 - Prob. 153PCh. 9.6 - Prob. 154PCh. 9.6 - Prob. 155PCh. 9.6 - Fig. P9.155 and P9.156 9.156 For the beam and...Ch. 9 - For the loading shown, determine (a) the equation...Ch. 9 - Prob. 158RPCh. 9 - For the beam and loading shown, determine (a) the...Ch. 9 - Determine the reaction at A and draw the bending...Ch. 9 - For the beam and loading shown, determine (a) the...Ch. 9 - For the beam and loading shown, determine (a) the...Ch. 9 - Beam CE rests on beam AB as shown. Knowing that a...Ch. 9 - The cantilever beam BC is attached to the steel...Ch. 9 - For the cantilever beam and loading shown,...Ch. 9 - Knowing that P = 4 kips, determine (a) the slope...Ch. 9 - For the beam and loading shown, determine (a) the...Ch. 9 - Determine the reaction at the roller support and...
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- For the beam shown: 1) Determine the reactions in terms of P. Modulus - E Area Moment of Inertia - I Заarrow_forwardFor the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the location of the maximum deflection, and (c) the maximum beam deflection. Assume that El is constant for the beam. Let w = 13 kN/m, L = 4.0 m, E = 180 GPa, and I = 130 x 106 mm“. B L Answer: (b) х %3 m (c) Vmax mmarrow_forwardStrength of Materialsarrow_forward
- PROBLEM 4.The beam AB consisting of a cast iron plate of uniform thickness, b, and length, L, is to support the distributed load w(x) shown a) Knowing that the beam is to be of constant strength (fully stressed beam), express h in terms of x, L and ho. b) Determine the smallest value of ho if L=800 mm, b=25 mm, wo=300 kN/m and oall=200 MPa. w-=WoCos(ITX/2L) A ho Barrow_forward6.36 Using Castigliano's method on the wire form shown determine the vertical deflection of point A considering bending only. The rigidity of the cross sec- tion is El. R Problem 6.36 Barrow_forwardFor the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the location of the maximum deflection, and (c) the maximum beam deflection. Assume that El is constant for the beam. Let w = 14 kN/m, L = 5.0 m, E = 190 GPa, and I = 105 x 106 mm4. Wo B L Answer: (Б) х %3 m (c) Vmax = mmarrow_forward
- Beam DE rests on the cantilever beam AC as shown. Knowing that a square rod of side 10 mm is used for each beam, determine the deflection at end C if the 25-N-m couple is applied (a) to end E of the beam DE, (b) to end C of the beam AC. Use E = 200 GPa. 10 mm D E A B 25 N-m 120 mm 180 mm ANS. (a) 5.94 mm ↓. (b) 6.75 mm ↓. 10 mmarrow_forwardProblem 3. (a) Draw the moment diagram for the beam. (b) Observing the direction of load and sign of the moment diagram, and knowledge of the boundary conditions, sketch the elastic curve, that is, the vertical deflection of the axial line thru the centroid of the beam section, (c) Determine the equation of the elastic curve for the beam using the x coordinate. (d) Specify the slope at A and the maximum deflection. El is constant. Mo L Barrow_forwardProblem 4.4 pleasearrow_forward
- 3. Determine the location and magnitude of the maximum deflection of the beam shown using: a. Double-integration Method b. Moment-Area Method c. Conjugate Beam Method 250 kN 6 m El = constant E = 200 GPa I = 462 (10*) mm*arrow_forwardFig. P9.78 E 9.79 and 9.80 For the uniform beam shown, determine (a) the reaction at A, (b) the reaction at B. ***** A Fig. P9.80 -L/2- Answer (a) 7 wL/128 1. (b)57 wL/128 1:9wL2/128. C -L/2- Barrow_forwardPROBLEM 9.11 Mg (a) Determine the location and magnitude of the maximum deflection of * beam AB. (b) Assuming that beam AB is a W360 x 64, L = 3.5 m, and E = 200 GPa, calculate the maximum allowable value of the applied moment M, if the maximum deflection is not to exceed 1 mm. B = 45.3 kN · marrow_forward
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