Homework Answers
clc
clear all
sigma_x = randi([-500 500]);
sigma_y = randi([-500 500]);
tau_xy = randi([-500,500]);
theta = randi([0 180]);
fprintf('sigma_x = %i\nsigma_y = %i\ntau_xy = %i\ntheta = %i
degree\n',...
sigma_x,sigma_y,tau_xy,theta);
sigma_n = 0.5*(sigma_x + sigma_y) + 0.5*(sigma_x -
sigma_y)*cosd(2*theta) + tau_xy*sind(2*theta);
tau_n = -0.5*(sigma_x - sigma_y)*sind(2*theta) +
tau_xy*cosd(2*theta);
fprintf('\nsigma_n = %0.3f\ntau_n = %0.3f\n',sigma_n,tau_n)
Add Answer to:
Plane stress transformation: Given randomly generated values of Ox, Oy, Txy and , calculate the normal...
A rectangular plate in plane stress is subjected to normal stresses Ox =50 MPa, Oy =...
A rectangular plate in plane stress is subjected to normal stresses Ox =50 MPa, Oy = 25 MPa, and shear stress Txy = -12.5 MPa. The ratio of the magnitudes of the principal stresses (01/02) is approximately: (A) 3.5 (B) 2 (C) 2.8 (0)4
An element in plane stress is subjected to stresses Ox, Oy, and Txy (see figure). The...
An element in plane stress is subjected to stresses Ox, Oy, and Txy (see figure). The material is aluminum with modulus of elasticity E:= 10 (10%) psi and Poisson's ratio v:=0.25. Hint: start with Hooke's Law for Plane Stress (Eq. 7-35 and 36) and the relationship between G and E! (a) Determine the strains for an element oriented at an angle e. (b) Determine the principal strains. (c) Determine the maximum shear strains. 0x := 3000 psi , := 600...
Problem 7 Determine the normal stress and shear stress acting on the inclined plane AB given:...
Problem 7 Determine the normal stress and shear stress acting on the inclined plane AB given: Ox = 45 psi Oy = 85 psi Txy = 15 psi O is 40 degrees (Use the stress orientation shown in the figure to determine the sign on the stress values.) a) normal stress: -56 psi, shear stress: 82 psi b) normal stress: -28 psi, shear stress: 75 psi c) normal stress: 17 psi, shear stress: 67 psi d) normal stress: 18 psi,...
Question 5 a) Determine the normal stress and shear stress acting on the inclined plane AB...
Question 5 a) Determine the normal stress and shear stress acting on the inclined plane AB as shown in Figure 7. Solve the problem using the stress transformation equations. Show the result on the sectioned element. B 45 MPa 80 MPa 45° Figure 7 [4 marks) Determine the principal stress, the maximum in-plane shear stress, and average normal stress for Figure 8. Specify the orientation of the element in each case. b) 200 MPa 500 MPa 350 MPa Figure 8
hello guys can u help me :) Question 1. For each of the plane-stress conditions given...
hello guys can u help me :)
Question 1. For each of the plane-stress conditions given below, using the matrix transformation law, determine the state of stress at the same point for an element rotated in the x-y plane 30° clockwise from its original position: (a) Ox = 200 MPa Oy = 400 MPa Txy = - 60 MPa (b) Ox = 300 MPa Oy = -180 MPa Txy = 320 MPa Question 2 my x2 The state of stress...
The given State of Stress is provided, the stresses are as follows: • ox= 15 KSI...
The given State of Stress is provided, the stresses are as follows: • ox= 15 KSI oy= 10 KSI • txy = 8 KSI Part 1 - For the state of stress described above: A. Draw the Mohr's Circle B. Determine the Radius of the Circle C. Find the coordinate Ō of its center D. Principal Stresses Plot all results above on the Mohr's Circle created under part A. Part 2 - Determine the following: A. Maximum In-Plane Shear Stress...
Problem 2 Below is shown a planar stress element for a given stress state o.. ....
Problem 2 Below is shown a planar stress element for a given stress state o.. . and known stresses) Using a free body diagam ("wedge" element) shown in Fig. (c) below, static equations of equilibrium, Fx =0 and Fy=0, and trig, Identities, Show that the normal and shear stresses at an arbitrary angle ,0x, Txy are defined by the following equations: NOTE: These are parametric equations for Mohr's Circle 0x = 6 0; + 0Os cos 2€ + sin 20...
Using expressions 2.29a and 2.29b from the textbook, plot normal stress (σθ) and shear stress (τθ) versus angle of an in...
Using expressions 2.29a and 2.29b from the textbook, plot normal
stress (σθ) and shear stress (τθ) versus angle of an inclined
stress element for a bar loaded by axial forces. Use Matlab or
Excel. What are slip bands? Why slip bands occur when mild steel
bars are loaded in tension. Explain your answer using the plotted
graphs.
results in the following expressions for the normal and shear stresses: (2-29a) (1 2 cos 20) (sin 20) 2 (2-29b) O sin 0...
A rectangular plate in plane stress is subjected to normal stresses Ox =50 MPa, Oy = 25 MPa, and shear stress Txy = -12.5 MPa. The ratio of the magnitudes of the principal stresses (01/02) is approximately: (A) 3.5 (B) 2 (C) 2.8 (0)4
An element in plane stress is subjected to stresses Ox, Oy, and Txy (see figure). The material is aluminum with modulus of elasticity E:= 10 (10%) psi and Poisson's ratio v:=0.25. Hint: start with Hooke's Law for Plane Stress (Eq. 7-35 and 36) and the relationship between G and E! (a) Determine the strains for an element oriented at an angle e. (b) Determine the principal strains. (c) Determine the maximum shear strains. 0x := 3000 psi , := 600...
Problem 7 Determine the normal stress and shear stress acting on the inclined plane AB given: Ox = 45 psi Oy = 85 psi Txy = 15 psi O is 40 degrees (Use the stress orientation shown in the figure to determine the sign on the stress values.) a) normal stress: -56 psi, shear stress: 82 psi b) normal stress: -28 psi, shear stress: 75 psi c) normal stress: 17 psi, shear stress: 67 psi d) normal stress: 18 psi,...
Question 5 a) Determine the normal stress and shear stress acting on the inclined plane AB as shown in Figure 7. Solve the problem using the stress transformation equations. Show the result on the sectioned element. B 45 MPa 80 MPa 45° Figure 7 [4 marks) Determine the principal stress, the maximum in-plane shear stress, and average normal stress for Figure 8. Specify the orientation of the element in each case. b) 200 MPa 500 MPa 350 MPa Figure 8
hello guys can u help me :)
Question 1. For each of the plane-stress conditions given below, using the matrix transformation law, determine the state of stress at the same point for an element rotated in the x-y plane 30° clockwise from its original position: (a) Ox = 200 MPa Oy = 400 MPa Txy = - 60 MPa (b) Ox = 300 MPa Oy = -180 MPa Txy = 320 MPa Question 2 my x2 The state of stress...
The given State of Stress is provided, the stresses are as follows: • ox= 15 KSI oy= 10 KSI • txy = 8 KSI Part 1 - For the state of stress described above: A. Draw the Mohr's Circle B. Determine the Radius of the Circle C. Find the coordinate Ō of its center D. Principal Stresses Plot all results above on the Mohr's Circle created under part A. Part 2 - Determine the following: A. Maximum In-Plane Shear Stress...
Problem 2 Below is shown a planar stress element for a given stress state o.. . and known stresses) Using a free body diagam ("wedge" element) shown in Fig. (c) below, static equations of equilibrium, Fx =0 and Fy=0, and trig, Identities, Show that the normal and shear stresses at an arbitrary angle ,0x, Txy are defined by the following equations: NOTE: These are parametric equations for Mohr's Circle 0x = 6 0; + 0Os cos 2€ + sin 20...
Using expressions 2.29a and 2.29b from the textbook, plot normal
stress (σθ) and shear stress (τθ) versus angle of an inclined
stress element for a bar loaded by axial forces. Use Matlab or
Excel. What are slip bands? Why slip bands occur when mild steel
bars are loaded in tension. Explain your answer using the plotted
graphs.
results in the following expressions for the normal and shear stresses: (2-29a) (1 2 cos 20) (sin 20) 2 (2-29b) O sin 0...
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