To determine The principal stresses acting at the point. The stress in the plane BC ( σ B C ) . Explanation Given information: Planes AB and BC are subjected to the stresses are shown in the given Figure. Calculation: The sign conventions for the stress components are explained below. The outward normal on the right-hand face of the element is representing as the positive x and x ' axes. The normal stress σ x and σ x ' are positive if it acts along the positive x and x ' axes. The normal stress σ y and σ y ' are positive if it acts along the positive y and y ' axes. The shear stress τ x y and τ x ' y ' are positive if it acts along the positive x and x ' axes. Sketch the forces and the plane on the sectioned element as shown in Figure 1. The angle θ is positive if it curls in the counterclockwise direction. Therefore, The value of θ is − 135 ° . Apply sign conventions to Figure 1. The value of normal stress are σ x = − 15 ksi and σ y = σ A C . The value of shear stress are τ x y = 5 ksi and τ x ' y ' = 6 ksi . The expression for shear stress for the plane oriented ( τ x ' y ' ) using the stress transformation equation is shown below: τ x ' y ' = − σ x − σ y 2 sin 2 θ + τ x y cos 2 θ (1) Substitute 6 ksi for τ x ' y ' , − 15 ksi for σ x , σ A C for σ y , − 135 ° for θ , and 5 ksi for τ x y in Equation (1). 6 = − − 15 + σ A C 2 sin 2 ( − 135 ° ) + 5 cos 2 ( − 135 ° ) 6 = 7.5 − 0.5 σ A C + 0 σ A C = − 3 ksi Find the in-plane principal stresses ( σ 1 ) and ( σ 2 ) using the relation: σ 1 , 2 = σ x + σ y 2 ± ( σ x − σ y 2 ) 2 + τ x y 2 (2) Substitute − 15 ksi for σ x , − 3 ksi for σ y , and 5 ksi for τ x y in Equation (2)

9th Edition

ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

See similar textbooks

Concept explainers

Die Stock

Die stock is expressed as the type of component which is utilized for fitting purposes while creating or shaping uniform threads on tubes, pipes, or screws. The die stock (die handle) has three screws around the adjustable part of a particular machine th…

Videos

Question

Chapter 9.3, Problem 9.20P

To determine

The principal stresses acting at the point.

The stress in the plane BC (σBC) .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.3, Problem 9.19P

Chapter 9.3, Problem 9.21P

Students have asked these similar questions

The resistance R and load effect S for a given failure mode are statistically independent random variables with marginal PDF's 1 fR (r) = 0≤r≤100 100' fs(s)=0.05e-0.05s (a) Determine the probability of failure by computing the probability content of the failure domain defined as {r

Please solve this problem as soon as possible My ID# 016948724

The gears shown in the figure have a diametral pitch of 2 teeth per inch and a 20° pressure angle. The pinion rotates at 1800 rev/min clockwise and transmits 200 hp through the idler pair to gear 5 on shaft c. What forces do gears 3 and 4 transmit to the idler shaft? TS I y 18T 32T This a 12 x 18T C 48T 5

Chapter 9 Solutions

Mechanics Of Materials, Si Edition

Ch. 9.3 - In each case, the state of stress x, y, xy...Ch. 9.3 - Given the state of stress shown on the element,...Ch. 9.3 - Determine the normal stress and shear stress...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - Also, find the corresponding orientation of the...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - Determine the maximum principal stress at point B.Ch. 9.3 - Determine the principal stress at point C.Ch. 9.3 - Prove that the sum of the normal stresses x + y =...Ch. 9.3 - 9-2. The state of stress at a point in a member is...

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.

The principal stresses acting at the point. The stress in the plane BC ( σ B C ) .

Concept explainers

Videos

The principal stresses acting at the point. The stress in the plane BC (σBC) .

Want to see the full answer?

Chapter 9 Solutions

The principal stresses acting at the point.

The stress in the plane BC (σBC) .