Explanation Given information: Load support P = 1500 N . The maximum shear stress in the pin is τ s = 150 MPa . Diameter of pins at B is d B =7 .5 mm . Diameter of pins at C is d C =6 .5 mm . Free body diagram of bike: For the system to be in equilibrium, ∑ F H = 0 ∑ F V = 0 ∑ M A = 0 Shear stress in pin is given by using the formula of shear stress. τ s = F s h e a r A s h e a r Shear area is given by: A s h e a r a t B = 2 × s h e a r i n g a r e a = 2 × π 4 d B 2 = 2 × π 4 × 7.5 2 mm 2 = 88.313 mm 2 A s h e a r a t C = 2 × s h e a r i n g a r e a = 2 × π 4 d C 2 = 2 × π 4 × 6.5 2 mm 2 = 66.333 mm 2 Factor of safety is given by: F O S = τ f a i l τ a l l o w a b l e Calculation: For the system to be in the horizontal equilibrium, ∑ F H = 0 F B D cos 60 ° + R C x = 0 R C x = − 3 2 F B D ............. 1 For the system to be in the vertical equilibrium, ∑ F V = 0 F B D sin 60 ° + R C y − P = 0 F B D sin 60 ° + R C y = P F B D × 1 2 + R C y = 1500 N ............. 2 Moment equilibrium about C . ∑ M C = 0 F B D cos 60 ° × 30 mm + F B D sin 60 ° × 100 mm − P × 400 mm = 0 3 2 F B D × 30 mm + F B D × 1 2 × 100 mm = P × 400 mm 75

11th Edition

ISBN: 9780137605385

Author: HIBBELER

Publisher: PEARSON

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Chapter 1.7, Problem 89P

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The factor of safety of pins B and C .

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Chapter 1.7, Problem 88P

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The factor of safety of pins B and C .

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The factor of safety of pins B and C .

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Chapter 1 Solutions