Explanation Given information: Refer the internal loadings at a section of the beam in the given Figure. The normal force in x -direction ( N x ) is − 80 kN . The shear force in y -direction ( V y ) is 60 kN . The moment in y -direction ( M y ) is − 0.5 kN ⋅ m . The moment in z -direction ( M z ) is 10 kN ⋅ m . Calculation: Find the area ( A ) of the wide flange section: A = ( 100 mm × 240 mm ) − ( 80 mm × 200 mm ) = 8 , 000 mm 2 Find the moment of inertia of the wide flange section in the z -direction ( I z ) : I z = 1 12 ( 100 mm ) ( 240 mm ) 3 − 1 12 ( 80 mm ) ( 200 mm ) 3 = 61.8667 × 10 6 mm 4 Find the moment of inertia of the wide flange section in the y -direction ( I y ) : I y = 2 [ 1 12 ( 20 mm ) ( 100 mm ) 3 ] + 1 12 ( 200 mm ) ( 20 mm ) 3 = 3.4667 × 10 6 mm 4 Find the first moment of area at point A ( Q A ) y : ( Q A ) y = 0 Find the normal stress at point A for the combined loadings using the relation: σ A = N A − M z y I z + M y z I y (1) Here, y is the centroid distance of the section in y -direction and z is the centroid distance of the section in z -direction. Refer the given Figure. The value of y is 120 mm and the value of z is 50 mm. Substitute − 80 kN for N , 8 , 000 mm 2 for A , 10 kN ⋅ m for M z , 120 mm for y , 61.8667 × 10 6 mm 4 for I z , − 0.5 kN ⋅ m for M y , 50 mm for z , and 3.4667 × 10 6 mm 4 for I y in Equation (1). σ A = − 80 kN 8 , 000 mm 2 − 10 kN ⋅ m × 120 mm 61.8667 × 10 6 mm 4 + − 0.5 kN ⋅ m × 50 mm 3.4667 × 10 6 mm 4 = [ − 80 kN × 10 3 N 1 kN 8 , 000 mm 2 − 10 kN ⋅ m × 10 3 N 1 kN × 10 3 mm 1 m × 120 mm 61

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain b…

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Chapter 14.3, Problem 24P

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Find the in-plane principal stresses at point A.

Find the maximum in-plane shear stress at point A.

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Chapter 14.3, Problem 23P

Chapter 14.3, Problem 25P

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Chapter 14 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 14.3 - In each ease, the state of stress x, y, xy...Ch. 14.3 - Given the state of stress shown on the element,...Ch. 14.3 - Determine the normal stress and shear stress...Ch. 14.3 - Prob. 2FP Ch. 14.3 - Determine the equivalent state of stress on an...Ch. 14.3 - Prob. 4FP Ch. 14.3 - The beam is subjected to the load at its end....Ch. 14.3 - Prob. 6FP Ch. 14.3 - Prove that the sum of the normal stresses x+y=x+y...Ch. 14.3 - Determine the stress components acting on the...

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Find the in-plane principal stresses at point A . Find the maximum in-plane shear stress at point A .

Solution Summary: The author calculates the in-plane principal stresses at point A and the maximum shear stress.

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Find the in-plane principal stresses at point A.

Find the maximum in-plane shear stress at point A.

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Chapter 14 Solutions

Find the in-plane principal stresses at point A . Find the maximum in-plane shear stress at point A .

Solution Summary: The author calculates the in-plane principal stresses at point A and the maximum shear stress.

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Find the in-plane principal stresses at point A. Find the maximum in-plane shear stress at point A.

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Chapter 14 Solutions

Find the in-plane principal stresses at point A.

Find the maximum in-plane shear stress at point A.