To determine The smallest dimension a of the timber. The spacing s of the bolt for the calculate value of a . Explanation Given information: The load on the simply supported beam is P = 16 kN . The allowable bending stress for the wood is σ allow = 30 MPa . The allowable shear stress for the wood is τ allow = 800 kPa . The shear resisted by each bolt is 2.5 kN . The cross-section width and depth of the beam are b = a and d = 2 a Calculation: Show the cross-section of the beam as shown in Figure 1. Refer to Figure 1. The cross-section width and depth of the beam are b = a and d = 2 a . Calculate the moment of inertia ( I ) as follows: I = b d 3 12 Substitute a mm for b and 2 a mm for d . I = a × ( 2 a ) 3 12 = 8 a 4 12 = 0.66667 a 4 Calculate the first moment of area ( Q max ) using the relation: Q max = y ¯ ′ A ′ (1) Here, A ′ is the shaded area and y ¯ ′ is the centroid of the shaded area. Refer to Figure 1. Substitute a 2 for y ¯ ′ and ( a × a ) for A ′ in Equation (1). Q max = a 2 ( a × a ) = a 2 × a 2 = 0.5 a 3 Show the loading in the beam as shown in Figure 1. Refer to Figure 2. Consider the reaction at the supports are denoted by A y and B y . The loading in the beam AB is symmetrical. Then, A y = B y = ( Total Loading on Joist 2 ) = ( 16 2 ) = 8 kN Calculate the shear force as follows: Calculate the shear force from point A : S F @ A = 8 kN Calculate the shear force from point C : S F @ L e f t o f s e c t i o n C = 8 kN S F @ R i g h t o f s e c t i o n C = 8 kN − 16 kN = − 8 kN Calculate the shear force from point B : S F @ B = − 8 kN + 8 kN = 0 Show the shear force diagram of the beam as shown in Figure 2. Refer to Figure 3. Consider the maximum shear force is denoted by V . Get the value of V = 8 kN . Calculate the bending moment at the sections passing through points A, B, and C . Consider the moment at section passing through points A, B, and C, is denoted by M A , M B and M C . Consider the support at A . M A = 0 Consider the left of the section passing through point B . M B = 8 × 3 = 24 kN ⋅ m Consider the support at C . M C = 0 Show the bending moment diagram of the beam as shown in Figure 3. Refer Figure 4. Consider the maximum bending moment is denoted by M max . Get the value of M max = 24 kN ⋅ m . Show the expression for the bending stress ( σ ) as follows: σ allow = M max c I (2) Here, σ allow is the allowable bending stress and c is the distance between the centroid of the cross-section and the outermost fiber. Calculate the value of c as follows: c = d 2 = 2 a 2 = a mm Substitute 30 MPa for σ allow , a for c , 24 kN ⋅ m for M max , and 0

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Combined Loading

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 11.2, Problem 11.30P

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The smallest dimension a of the timber.

The spacing s of the bolt for the calculate value of a.

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Chapter 11.2, Problem 11.29P

Chapter 11.4, Problem 11.31P

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Mechanics of Materials

Ch. 11.2 - Determine the minimum dimension a to the nearest...Ch. 11.2 - of the rod to safely support the load. The rod is...Ch. 11.2 - The wood has an allowable normal stress of allow =...Ch. 11.2 - of the beam's cross section to safely support the...Ch. 11.2 - Determine the minimum dimension b to the nearest...Ch. 11.2 - The beam is made of steel having an allowable...Ch. 11.2 - Determine its dimensions if it is to be...Ch. 11.2 - Determine the minimum width of the beam to the...Ch. 11.2 - if P=10 kip.Ch. 11.2 - If the allowable bending stress is allow = 22 ksi...

Ch. 11.2 - The allowable bending stress is allow = 24 ksi and...Ch. 11.2 - The allowable bending stress is allow = 22 ksi and...Ch. 11.2 - 11–7. Draw the shear and moment diagrams for the...Ch. 11.2 - *11–8. The simply supported beam is made of timber...Ch. 11.2 - The beam has an allowable normal stress of allow =...Ch. 11.2 - The beam has an allowable normal stress of allow...Ch. 11.2 - 11–11. The timber beam is to be loaded as shown....Ch. 11.2 - If each beam is to be designed to carry 90 lb/ft...Ch. 11.2 - 11–13. Select the lightest steel wide-flange beam...Ch. 11.2 - 11–14. Select the lightest-weight steel...Ch. 11.2 - Prob. 11.15P Ch. 11.2 - The beam has an allowable normal stress of allow....Ch. 11.2 - Determine the maximum cable force P that can...Ch. 11.2 - to safely support the load. The wood has an...Ch. 11.2 - and the wood has an allowable normal stress of...Ch. 11.2 - Prob. 11.20P Ch. 11.2 - Prob. 11.21P Ch. 11.2 - Prob. 11.22P Ch. 11.2 - 11–23. The beam is constructed from three boards...Ch. 11.2 - Prob. 11.24P Ch. 11.2 - Prob. 11.25P Ch. 11.2 - Select the lightest-weight wide-flange beam from...Ch. 11.2 - Prob. 11.27P Ch. 11.2 - * 11–28. The joist AB used in housing construction...Ch. 11.2 - If the maximum bending stress is not to exceed...Ch. 11.2 - 11–30. The simply supported beam supports a load...Ch. 11.4 - Determine the variation in the width was a...Ch. 11.4 - Prob. 11.32P Ch. 11.4 - Prob. 11.33P Ch. 11.4 - The beam is made from a plate that has a constant...Ch. 11.4 - Determine the variation in the depth d of a...Ch. 11.4 - Determine the variation of the radius r of the...Ch. 11.4 - Prob. 11.37P Ch. 11.4 - Determine the variation in the width b as a...Ch. 11.4 - The tubular shaft has an inner diameter of 15 mm....Ch. 11.4 - Prob. 11.40P Ch. 11.4 - Prob. 11.41P Ch. 11.4 - Prob. 11.42P Ch. 11.4 - Prob. 11.43P Ch. 11.4 - Prob. 11.44P Ch. 11.4 - Prob. 11.45P Ch. 11.4 - Prob. 11.46P Ch. 11 - The cantilevered beam has a circular cross...Ch. 11 - Select the lightest-weight wide-flange overhanging...Ch. 11 - Prob. 11.49RP Ch. 11 - Determine the shaft's diameter to the nearest...Ch. 11 - Select the lightest-weight wide-flange beam from...Ch. 11 - The simply supported joist is used in the...Ch. 11 - The simply supported joist is used in the...Ch. 11 - by 4-in. pieces of wood braced as shown. If the...

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The smallest dimension a of the timber.

The spacing s of the bolt for the calculate value of a.