(a) Explanation Given information: Consider the area of cross-section is denoted by A . Consider the moment of inertia of the cross-section about the x and z axis is denoted by I x and I z . Consider the moment about the x and z axis is denoted by M x and M z . Calculation: Show the expression for the radius of gyration of the cross section about x and z axis as shown below: r x 2 = I x A r z 2 = I z A } (1) Show the expression for the moment created by the load P about x and z axis as shown below: M x = P z A M z = − P x A } (2) Show the expression for the stress ( σ E ) at the point E as shown below: σ E = − P A + ( M z ) x E ( I z ) − ( M x ) z E ( I x ) (3) Modify Equation (3) using Equation (1) and (2) . σ E = − P A + ( − P x A ) x E ( A r z 2 ) − ( P z A ) z E ( A r x 2 ) = − P A − P x A x E A r z 2 − P z A z E A r x 2 (b) To determine Show the stress at point A is zero when a vertical force Q is applied on line BD .

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

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Chapter 4.9, Problem 160P

(a)

To determine

Show the Equation of neutral axis BD, when a vertical force P is applied on the point A is

(xArz2)x+(zArx2)z=−1

Here, rz and rx are the radius of gyration of the cross-section about z and x axis.

(b)

To determine

Show the stress at point A is zero when a vertical force Q is applied on line BD.

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Chapter 4.9, Problem 159P

Chapter 4.10, Problem 161P

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Show the Equation of neutral axis BD , when a vertical force P is applied on the point A is ( x A r z 2 ) x + ( z A r x 2 ) z = − 1 Here, r z and r x are the radius of gyration of the cross-section about z and x axis.

Solution Summary: The author shows the Equation of neutral axis BD, when a vertical force P is applied on the point A.

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Show the Equation of neutral axis BD, when a vertical force P is applied on the point A is

(xArz2)x+(zArx2)z=−1

Here, rz and rx are the radius of gyration of the cross-section about z and x axis.

Show the stress at point A is zero when a vertical force Q is applied on line BD.

Want to see the full answer?

Chapter 4 Solutions

Show the Equation of neutral axis BD , when a vertical force P is applied on the point A is ( x A r z 2 ) x + ( z A r x 2 ) z = − 1 Here, r z and r x are the radius of gyration of the cross-section about z and x axis.

Solution Summary: The author shows the Equation of neutral axis BD, when a vertical force P is applied on the point A.

Concept explainers

Videos

Show the Equation of neutral axis BD, when a vertical force P is applied on the point A is (xArz2)x+(zArx2)z=−1 Here, rz and rx are the radius of gyration of the cross-section about z and x axis.

Show the stress at point A is zero when a vertical force Q is applied on line BD.

Want to see the full answer?

Chapter 4 Solutions

Show the Equation of neutral axis BD, when a vertical force P is applied on the point A is

(xArz2)x+(zArx2)z=−1

Here, rz and rx are the radius of gyration of the cross-section about z and x axis.