(a) Explanation Given information: Refer to problem 5.76 in chapter 5 in the textbook. The allowable bending stress is 24 ksi . The rolled steel section is S 15 × 42.9 . Calculation: Show the free-body diagram of the beam as in Figure 1. Determine the vertical reaction at point B by taking moment at point E . ∑ M E = 0 48 ( 12 ) − B y ( 10 ) + 48 ( 8 ) + 48 ( 2 ) = 0 576 − 10 B y + 384 + 96 = 0 B y = 105.6 kips Determine the vertical reaction at point E by resolving the vertical component of forces. ∑ F y = 0 − 48 + B y − 48 − 48 + E y = 0 − 48 + 105.6 − 96 + E y = 0 E y = 38.4 kips Shear force: Show the calculation of shear force as follows; V A = − 48 kips V B − V A = 0 V B L e f t = V A = − 48 kips V B R i g h t = − 48 + 105.6 = 57.6 kips V C − V B = 0 V C L e f t = 0 + V B = 0 + 57.6 = 57.6 kips V C R i g h t = 57.6 − 48 = 9.6 kips V D − V C = 0 V D L e f t = V C = 9.6 kips V D R i g h t = 9.6 − 48 = − 38.4 kips V E − V D = 0 V E = V D = − 38.4 kips Show the calculated shear force values as in Table 1. Location ( x ) ft Shear force ( V ) kips A –48 B (Left) –48 B (Right) 57.6 C (Left) 57.6 C (Right) 9.6 D (Left) 9.6 D (Right) –38.4 E –38.4 Plot the shear force diagram as in Figure 2. Bending moment: Show the calculation of the bending moment as follows; M A = 0 M B − M A = − 48 × 2 M B = − 96 + M A = − 96 + 0 = − 96 kips-ft M C − M B = 57 (b) To determine The maximum value of principal stress σ max at the junction of a flange and the web

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ISBN: 8220102804487

Author: BEER

Publisher: YUZU

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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 8.2, Problem 12P

(a)

To determine

The actual value of σm in the beam.

(b)

To determine

The maximum value of principal stress σmax at the junction of a flange and the web

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Chapter 8.2, Problem 11P

Chapter 8.2, Problem 13P

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Chapter 8 Solutions

EBK MECHANICS OF MATERIALS

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The actual value of σ m in the beam.

Solution Summary: The author explains how to calculate the shear force by resolving the vertical component of forces.