Po AT Problem 2. The deformable bar of length 2a, Young's modulus E, coefficient of thermal expansion a, and cross-sectional area A is subjected to a distributed axial force per unit length with constant intensity po in the domain from 0≤x≤ a, and a uniform temperature change of AT in the shaded region from a ≤x≤ 2a. (a) Determine the displacement ua at x = a. (b) Determine the displacement uza at x = 2a. a a

Po AT Problem 2. The deformable bar of length 2a, Young's modulus E, coefficient of thermal expansion a, and cross-sectional area A is subjected to a distributed axial force per unit length with constant intensity po in the domain from 0≤x≤ a, and a uniform temperature change of AT in the shaded region from a ≤x≤ 2a. (a) Determine the displacement ua at x = a. (b) Determine the displacement uza at x = 2a. a a

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.6.7P: A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The...

See similar textbooks

Similar questions

A very thick structure is subjected to certain traction boundary conditions on its surface. The cross-section and the applied load do not vary with the z-coordinate. The following stress function is proposed for this problem: -y p(x,y) = Sin (x) (A x²e + B e") (i) use the biharmonic equation to find restrictions, if any, on values of A and B (ii) calculate all stress components (iii) calculate all strain components in terms of A, B, and C as well as the Young modulus and Poisson's ratio E and y, respectively. (iv) check that the equilibrium equations are satisfied (v) determine the traction boundary conditions at x =± a and y=+b
Po ΔΤ' Problem 2. The deformable bar of length 2a, Young's modulus E, coefficient of thermal expansion a, and cross-sectional area A is subjected to a distributed axial force per unit length with constant intensity po in the domain from 0≤x≤ a, and a uniform temperature change of AT in the shaded region from a ≤ x ≤ 2a. (a) Determine the displacement ua at x = a. (b) Determine the displacement uza at x = 2a. a a
Problem 1 Consider a plate formed by a non-homogeneous material with Young's modulus E(z) = Eo-zE, with Eo, E1 > 0 and Poisson's ratio v. The plate has total thickness h, the reference plane is located at the center of the plate, and N and Ny are applied at z = 0. Find the stiffness matrix of the plate.
H.W 1. Consider a two degree of freedom bar elements as shown in figure. Using finite element method to formulate the equilibrium equation of it. If the cross sectional area is 12 mm and E=200 GN/m². 20KN +30KN 15KN 300 * 600- + 350 All Dimension in mm 2. Consider a two degree of freedom bar element as shown in figure. Using finite element method to formulate the equilibrium equation of it, and then estimate the stress distributions. If Esteel-200 GN/m, Ecopper 110GN/m and EAL= 120 GN/m?. d=3 Steel AL Соpper 20KN - 30KN →15KN 300 * 200 - 400 * 350 All Dimension in mm
The plate A thin plate of linear elastic materials (E = 200 GPa, 0.25) is in plane stress (o, = Txz = Tyz = 0). V = heated by 100 °F and the thermal expansion efficient of the plate is, a = 8 x 10 eidsdon 50 MPa 1 The plate is also compressed between two perfectly smooth surfaces as shown in the figure. °F 50 MPa Find the following: a. The non-zero stress in the plate. b. The change in c. The strain Exa the thickness direction of the 400 mm plate, and change in the thickness of the the initial thickness is 4 mm. 200 mm
5 An infismall element is p ven on a plone, where =0. where Jz = 0. 120uPa 120MPQ 80Mla Modulus of elosticities are 60 G la ond y ohrectrons, respectively. radro's 24 GPa in x and dire The 0.2 ond 0.4e parson in x ond ore direc thens, respectively. Determane the stroin in x ond y directhens.
Pipe Pa Fluid Rigid rock Figure 1: A pipe embedded in rigid rock. Consider an isotropic linear elastic pipe of inner radius a and outer radius b embedded in rigid (i.e., non-deforming) material and holding a fluid at pressure Pa. Ignore the effects of gravity. This may be a good model for a PVC pipe embedded in rock or concrete. Assume the problem is symmetric and that strains out of the plane shown in Fig. 1are zero. (a) What state of strain exists in the pipe, plane strain or plane stress? (b) Determine the stress components, orr and σ00, and displacements, ur, in the pipe. (c) Is the stress difference orr - 000| greatest at r=a or r = b? Note: the location of the greatest stress difference is where plasticity will occur first (to be covered later in class).
H= 55mm A= 40mm R1 R2 B= 55mm C= 50mm R1=13mm H P=2000 N R2= 15mm A B Figure QI: A rectangular plate with holes
1.4-7 The data shown in the table below were obtained from a tensile test of high-strength steel. The test specimen had a diameter of 13 mm and a gage length of 50 mm (see figure for Prob. 1.4-3). At fracture, the elongation between the gage marks was 3.0 mm and the minimum diameter was 10.7 mm. Plot the conventional stress-strain curve for the steefor the steel and determine the proportional limit, modulus of elastics of elastic- ity (i.e., the slope of the initial part of the stress-strain,tress-strain curve), yield stress at 0.1% offset, ultimate stress, percent, elongation in 50 mm, and percent reduction in area. 'ess, percent area. TENSILE-TEST DATA FOR PROB. 1.4-7 Elongation (mm) 0.005 0.015 0.048 Load (kN) 5 10 30 50 0.084 60 0.099 64.5 0.109 67.0 0.119 68.0 0.137 69.0 0.160 70.0 0.229 72.0 0.259 76.0 0.330 84.0 0.584 92.0 0.853 100.0 1.288 112.0 2.814 113.0 Fracture
A thin plate of linear elastic materials (E = 200 GPa, 0.25) is in plane stress (a, = Txz = Tyz = 0). The plate is heated by 100 °F and the thermal V = expansion efficient of the plate is, a = 8 x 10 6. °F The plate is also compressed between two rigid, perfectly smooth surfaces as shown in the figure. 50 MPa 150 MPa Find the following: a. The non-zero stress in the plate. b. The change in the dimension in X- direction. c. The strain in the thickness direction of the 400 mm plate, ɛ, and change in the thickness of the plate f the initial thickness is 4 mm. 200 mm
A solid bar of length L = 4 m and diameter 200 mm is heated from 20 to 320 degrees celsius and restrained between two solid immovable walls. Young's modulus of the material is 90 GPa and the coefficient of thermal expansion is 22 x 10-6/°C. →Calculate the thermal strain, e, in micro-strain correct to two decimal places. micro-strain. Calculate the thermal stress, o, in megapascals (MPa) correct to two decimal places. E: σ: MPa. Hence calculate the force exerted by the bar in meganewtons (MN) correct to two decimal places: F MN. L
Problem 2 Consider a plate formed by a homogeneous material with Young's modulus E, and Poisson's ratio v. The plate has total thickness h, the reference plane is located at the center of the plate, and N and Ny are applied at z = -h/2. Find the stiffness matrix of the plate.