Explanation Given information: The moments of inertia are I ′ z = 31.7 ( 10 − 6 ) m 4 , I ′ y = 114 ( 10 − 6 ) m 4 , I y ′ z ′ = − 15.8 ( 10 − 6 ) m 4 where z ′ and y ′ are the principal axes. The principal moment of inertia of the member’s cross sectional area are I y = 117 ( 10 − 6 ) m 4 and I z = 28.8 ( 10 − 6 ) m 4 , calculated about the principal axis of inertia y and z , respectively. The section is subjected to a moment of M = 15 kN-m . Calculation: Show the free body diagram of the section for resultant moments as in Figure 1. The resultant moment in y ′ -direction is as follows: M y ′ = 0 The resultant moment in z ′ -direction is as follows: M z ′ = 15 kN-m Determine the resultant normal stress at any point on the cross section using the equation. σ = − ( M z ′ I y ′ + M y ′ I y ′ z ′ ) y A ′ + ( M y ′ I z ′ + M z ′ I y ′ z ′ ) z A ′ I y ′ I z ′ − I y ′ z ′ 2 (1) Here, σ is the normal stress at the point. Tensile stress is positive and compressive stress is negative. Stress at point A : Show the coordinates of point A as in Figure 2. The distance in y ′ -direction is as follows: y A ′ = 60 mm × 1 m 1,000 mm = 0.06 m The distance in z ′ -direction is as follows: z A ′ = − 140 mm × 1 m 1,000 mm = − 0

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…

Videos

Question

Chapter 11.5, Problem 104P

To determine

Find the stress produced at point A.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.5, Problem 103P

Chapter 11, Problem 1RP

Students have asked these similar questions

If you have a spring mass damper system, given by m*x_double_dot + c*x_dot + kx = 0 where m, c, k (all positive scalars) are the mass, damper coefficient, and spring coefficient, respectively. x ∈ R represents the displacement of the mass. Using linear stability analysis, show that the system is asymptotically stable. Hint: stability of a linear system z_dot = Az is characterized by the eigenvalues of A.

What would the electropneumatic diagram of a circuit with the sequence a+b+c+(a-b-c-) look like?

### What would the electropneumatic diagram of a circuit with the sequence a+b+c+(a-b-c-) look like, with a counter, in the fluidsim?

Chapter 11 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 11.2 - In each case, the beam is subjected to the...Ch. 11.2 - In each ease, express the shear and moment...Ch. 11.2 - In each ease, express the shear and moment...Ch. 11.2 - In each ease, express the shear and moment...Ch. 11.2 - In each ease, express the shear and moment...Ch. 11.2 - Prob. 5FP Ch. 11.2 - Prob. 6FP Ch. 11.2 - In each ease, draw the shear and moment diagrams...Ch. 11.2 - Prob. 8FP Ch. 11.2 - Prob. 1P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Find the stress produced at point A .

Solution Summary: The author shows the free body diagram of the section for resultant moments as in Figure 1.

Concept explainers

Videos

Find the stress produced at point A.

Want to see the full answer?

Chapter 11 Solutions