Explanation Given Information: The wide flange beam is subjected to a 50 kN force. Calculation: Calculate the normal stress ( σ B ) acting at point B using the relation: σ B = − M y I (1) Here, M is the moment, y is the centroid distance to point B , and I is the moment of inertia. Sketch the forces and moments at point B as shown in Figure 1. Apply Equilibrium equations to find the value of forces and moment at point B . Sum of horizontal forces at point B is equal to 0. Σ F x = 0 N = 0 Sum of vertical forces at point B is equal to 0. Σ F y = 0 V − 50 = 0 V = 50 kN Sum of moments at point B is equal to 0. Σ M = 0 M − 50 ( 3 ) = 0 M = 150 kN ⋅ m Find the moment of inertia of the section ( I ) using the given Figure: I = 1 12 ( 200 mm ) ( 274 mm ) 3 − 1 12 ( 190 mm ) ( 250 mm ) 3 = 95.451233 × 10 6 mm 4 Find the first moment of area at point B ( Q B ) using the relation: Q B = y ¯ ' A ' (2) Here, y ¯ ' is the centroid distance to point B and A ' is the area from centroid to point B . The value of y ¯ ' is 131 mm . Q B = 131 mm ( 12 mm ) ( 200 mm ) = 0.3144 × 10 6 mm 3 Substitute 150 kN ⋅ m for M , 125 mm for y , and 95.451233 × 10 6 mm 4 for I in Equation (1). σ B = − ( 150 kN ⋅ m ) ( 125 mm ) 95.451233 × 10 6 mm 4 = − ( 150 kN ⋅ m × 10 3 N 1 kN × 10 3 mm 1 m ) ( 125 mm ) 95.451233 × 10 6 mm 4 = − 196.43 N mm 2 = − 196.43 MPa Find the shear stress ( τ B ) at point B using the relation: τ B = V Q B I t Here, t is the thickness of the web

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 14.3, Problem 40P

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Find the principal stresses at point B.

Find the shear stress using the shear formula.

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Chapter 14.3, Problem 39P

Chapter 14.3, Problem 41P

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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 principal stresses at point B . Find the shear stress using the shear formula.

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Find the principal stresses at point B.

Find the shear stress using the shear formula.

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Chapter 14 Solutions

Find the principal stresses at point B . Find the shear stress using the shear formula.

Solution Summary: The author calculates the principal stresses at point B using the shear formula.

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Find the principal stresses at point B. Find the shear stress using the shear formula.

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Chapter 14 Solutions

Find the principal stresses at point B.

Find the shear stress using the shear formula.