Explanation Given information: The bearings at A and D exert only y and z components. The allowable shear stress is τ allow = 60 MPa . Calculation: Sketch the Free Body Diagram of the beam as shown in Figure 1. Refer to Figure 1. Let A y is the reaction at point A about y axis, D x is the reaction at point B about x axis, A x is the reaction at point A about x axis, and D y is the reaction at point B about y axis. Find the reaction at the support as shown below. Apply Equations of Equilibrium as shown below. Take moment about A along y axis is Equal to zero. ∑ M A y = 0 ( 3 × 200 ) + ( D x × 950 ) + 150 − 150 = 0 600 + 950 D x = 0 950 D x = 600 D x = − 0.632 kN Summation of vertical forces is equal to zero. ∑ F x = 0 A x + 3 − 0.632 = 0 A x = − 2.368 kN Take moment about A about x axis. ( − 2 × 600 ) + ( D y × 950 ) = 0 − 1 , 200 + 950 D y = 0 950 D y = 1 , 200 D y = 1.263 kN Summation vertical forces are equal to zero. ∑ F y = 0 A y − 2 + 1.263 = 0 A y = 0.737 kN Sketch the Free Body Diagram with values as shown in Figure 2. Refer to Figure 2: Find the moment about y axis as follows: Moment at point D : M D = 0 Moment at point C : M C = 1.263 × 350 = 442.05 kN ⋅ mm × 1 , 000 N 1 kN × 1 m 1 , 000 mm = 442.05 N ⋅ m Moment at point B : M B = 1.263 × 750 − 2 × 400 = 147.25 kN ⋅ mm × 1 , 000 N 1 kN × 1 m 1 , 000 mm = 147.25 N ⋅ m Moment at point A : M A = 0 Sketch the bending moment B and C critical location as shown in Figure 3. Find the moment about z axis as follows: Moment at point B : M B = 0 Moment at point C : M C = 0.632 × 350 = 221.2 kN ⋅ mm × 1 , 000 N 1 kN × 1 m 1 , 000 mm = 221

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ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Buckling of columns

The column is described as a vertical member of the structure that carries an axial compressive load, and buckling is a lateral deformation of the column under the application of load.

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Chapter 11.4, Problem 11.45P

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The smallest diameter of the shaft.

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Chapter 11 Solutions

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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