(a) Explanation Calculate the normal stress ( σ A ) acting at point A using the relation: σ A = P A + M x y I x + M y x I y (1) Here, P is the axial load, A is the area, M x is the moment in the x -direction, y is the distance in y -direction from centroid to point A , and I x is the moment of inertia in the x -direction, M y is the moment in the y-direction, x is the distance in x -direction from centroid to point A , and I y is the moment of inertia in the y -direction. Sketch the forces and moments at point A as shown in Figure 1. Apply Equilibrium equations to find the value of forces and moment at point A . Sum of forces in x -direction at point A is equal to 0. Σ F x = 0 V x = 400 lb Sum of forces in y -direction at point A is equal to 0. Σ F y = 0 V y = 500 lb Sum of forces in z -direction at point A is equal to 0. Σ F z = 0 N z = 900 lb Sum of moments in y -direction is equal to 0. Σ M y = 0 M y = 400 × 9 in . M y = 3 , 600 lb ⋅ in . Sum of moments in x -direction is equal to 0. Σ M x = 0 M x = 400 × 9 in . M x = 4 , 500 lb ⋅ in . Find the moment of inertia of the section ( I x = I y ) using the given cross section: I x = I y = 1 12 ( 3 in . ) ( 3 in . ) 3 = 6.75 in 4 Find the area of the section ( A ) : A = ( 3 in . ) ( 3 in . ) = 9 in 2 Find the first moment of area at point A ( Q A ) x in the x -direction using the relation: ( Q A ) x = y ¯ ' A ' Here, y ¯ ' is the centroid distance to point A and A ' is the area from centroid to point A . Sketch the section and the centroid distance as shown in Figure 2. Refer Figure 2 for values of y ¯ ' . Q A = 1 in ( 1 in ) ( 3 in ) = 3 in 3 Substitute − 900 lb for P , 9 in 2 for A , 4 , 500 lb ⋅ in for M x , 1.5 in . for y , 6.75 in 4 for I x , − 3 , 600 lb ⋅ in for M y , 0.5 in . for x , 6.75 in 4 for I y in Equation (1). σ A = − 900 lb 9 in 2 + ( 4 , 500 lb ⋅ in ) ( 1.5 in . ) 6.75 in 4 − ( 3 , 600 lb ⋅ in ) ( 0.5 in . ) 6.75 in 4 = 633.33 psi Find the shear stress ( τ A ) at point A using the relation: τ z x = V Q I t Here, t is the thickness (b) To determine Find the maximum in-plane shear stress developed at point A .

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

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…

Videos

Question

Chapter 14.4, Problem 75P

(a)

To determine

Find the principal stresses at point A.

(b)

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 74P

Chapter 14.5, Problem 76P

Students have asked these similar questions

1 in. 4. The rod has a diameter of 40 mm. If it is subjected to the force system shown, determine the state of stress (all the stress components) at point A. 1500 N 600 N 300 mm 100 N·m 800 N 100 mm

Determine the maximum distance d to the edge of the plate at which the force P can be applied so that it produces no compressive stresses on the plate at section a–a. The plate has a thickness of 20 mm and P acts along thecenterline of this thickness.

Assume that the magnitude of the vertical force P is 2.5 kN. Determine the stress at point A and B

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...

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 principal stresses at point A .

Solution Summary: The author explains how to find the principal stresses at point A and calculate the normal stress using the relation: (sigma_A).