Explanation Given information: Set the angle of the moment from y axis is θ = 45 ° . Explanation: Show the free-body diagram of the square cross section as in Figure 1. Determine the moment of inertia in y and z - direction of the square cross section using the formula. I z = I y = b d 3 12 Here, b is width of the square section and d is depth of the square section. Substitute 250 mm for b and 250 mm for d . I z = I y = 250 mm × 1 m 1,000 mm × ( 250 mm × 1 m 1,000 mm ) 3 12 = 0.325521 × 10 − 3 m 4 Show the free body diagram of the square cross section for resultant moments as in Figure 2. The resultant moment in y -direction is as follows: M y = M cos θ = 850 × cos 45 ° = 601.04 N-m The resultant moment in z -direction is as follows: M z = M sin θ = 850 × sin 45 ° = 601.04 N-m Determine the resultant normal stress at any point on the cross section using the equation. σ = − M z y I z + M y z I y (1) Here, σ is the normal stress at the point. Tensile stress is positive and compressive stress is negative. Stress at point A : The distance in y -direction is y A = − 125 mm . The distance in z -direction is z A = − 125 mm . Thus, the y and z coordinates of point A is (–125 mm, –125 mm). Substitute 601.04 N-m for M z , –125 mm for y , 0.325521 × 10 − 3 m 4 for I z , 601.04 N-m for M y , –125 mm for z , and 0.325521 × 10 − 3 m 4 for I y in Equation (1). σ A = − 601.04 × ( − 125 mm × 1 m 1,000 mm ) 0.325521 × 10 − 3 + 601.04 × ( − 125 mm × 1 m 1,000 mm ) 0.325521 × 10 − 3 = − 230 , 799.4 + 230 , 799.4 = 0 Thus, the stress at point A is σ A = 0 _ . Stress at point B : The distance in y -direction is y B = − 125 mm . The distance in z -direction is z B = 125 mm . Thus, the y and z coordinates of point B is (–125 mm, 125 mm). Substitute 601.04 N-m for M z , –125 mm for y , 0.325521 × 10 − 3 m 4 for I z , 601.04 N-m for M y , 125 mm for z , and 0.325521 × 10 − 3 m 4 for I y in Equation (1). σ B = − 601.04 × ( − 125 mm × 1 m 1,000 mm ) 0

5th Edition

ISBN: 8220102955295

Author: HIBBELER

Publisher: PEARSON

See similar textbooks

Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

Videos

Question

Chapter 11.5, Problem 96P

To determine

Find the stress at each corner of the square cross section.

Sketch the stress distribution.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.5, Problem 15FP

Chapter 11.5, Problem 97P

Students have asked these similar questions

Only 100% sure experts solve it correct complete solutions okk don't use guidelines or ai answers okk will dislike okkk. Only human experts solved it

Airplanes A and B, flying at constant velocity and at the same altitude, are tracking the eye of hurricane C. The relative velocity of C with respect to A is 300 kph 65.0° South of West, and the relative velocity of C with respect to B is 375 kph 50.0° South of East. A 120.0 km B 1N 1. Determine the relative velocity of B with respect to A. A ground-based radar indicates that hurricane C is moving at a speed of 40.0 kph due north. 2. Determine the velocity of airplane A. 3. Determine the velocity of airplane B. Consider that at the start of the tracking expedition, the distance between the planes is 120.0 km and their initial positions are horizontally collinear. 4. Given the velocities obtained in items 2 and 3, should the pilots of planes A and B be concerned whether the planes will collide at any given time? Prove using pertinent calculations. (Hint: x = x + vt) 0

Only 100% sure experts solve it correct complete solutions okk don't use guidelines or ai answers okk will dislike okkk.

Chapter 11 Solutions

EBK STATICS AND MECHANICS OF MATERIALS

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 at each corner of the square cross section. Sketch the stress distribution.

Solution Summary: The author shows the free-body diagram of the square cross section as in Figure 1. Determine the moment of inertia in y and z- direction using the formula.