Explanation The allowable normal stress in the beam is σ a l l = 150 MPa . Show the free-body diagram of the prismatic beam as in Figure 1. Determine the vertical reaction at point C by taking moment at point A . ∑ M A = 0 C y ( 4.8 ) − P ( 7 ) = 0 C y = 1.45833 P Determine the vertical reaction at point A by resolving the vertical component of forces. ∑ F y = 0 − A y + C y − P = 0 − A y + 1.45833 P − P = 0 A y = 0.45833 P Allowable load based on sections AB and CD : Show the free-body diagram of the section AB as in Figure 2. Determine the moment at point B by taking moment about point B . ∑ M B = 0 M B + 0.45833 P ( 2.55 ) = 0 M B = − 1.1687415 P Show the free-body diagram of the section DE as in Figure 3. Determine the moment at point D by taking moment about point D . ∑ M D = 0 − M D − P ( 0.95 ) = 0 M D = − 0.95 P The moments at the points B and D are critical. | M D | < | M B | . Thus, the moment at point B controls. Refer to Appendix C “Properties of Rolled-Steel Sections” in the textbook. The section modulus of the W 410 × 85 section is S = 1510 × 10 3 mm 3 Determine the largest concentrated load ( P ) of the beam using the relation. σ a l l = | M B | S Here, the allowable stress of the beam is σ a l l . Substitute 150 MPa for σ a l l , 1.1687415 P for | M B | , and 1510 × 10 3 mm 3 for S . 150 MPa × 10 6 Pa 1 MPa = 1.1687415 P 1510 × 10 3 mm 3 × ( 1 m 1000 mm ) 3 P = 193.8 × 10 3 N × 1 kN 10 3 N = 193.8 kN Allowable load based on BCD : Show the free-body diagram of the section CDE as in Figure 4. Determine the moment at point C by taking moment about point C . ∑ M C = 0 − M C − P ( 2.2 ) = 0 M C = − 2.2 P Show the free-body diagram of the cross section of the beam as in Figure 5. Refer to Appendix C “Properties of Rolled-Steel Sections” in the textbook

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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Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 5.5, Problem 143P

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Find the largest concentrated load P acting at point E.

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Chapter 5.5, Problem 142P

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Chapter 5 Solutions

Mechanics of Materials, 7th Edition

Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.7 and 5.8 Draw the shear and bending-moment...Ch. 5.1 - 5.7 and 5.8 Draw the shear and bending-moment...Ch. 5.1 - 5.9 and 5.10 Draw the shear and bending-moment...Ch. 5.1 - 5.9 and 5.10 Draw the shear and bending-moment...

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Find the largest concentrated load P acting at point E .

Solution Summary: The author shows the free-body diagram of the prismatic beam as in Figure 1. Determine the vertical reaction at point C by taking moment about point A.

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