Solve for the axial displacement and stress in the tapered bar shown in Figure P3-12 using one and then two constant-area elements. Evaluate the area at the center of each element length. Use that area for each element. Let Ao = 2 in2 , L= 20 in., E = 10 106 psi, and P = 1000 lb. Compare your finite element solutions with the exact solution. A(x) = Ao(1 + £) P- Figure P3-12

Solve for the axial displacement and stress in the tapered bar shown in Figure P3-12 using one and then two constant-area elements. Evaluate the area at the center of each element length. Use that area for each element. Let Ao = 2 in2 , L= 20 in., E = 10 106 psi, and P = 1000 lb. Compare your finite element solutions with the exact solution. A(x) = Ao(1 + £) P- Figure P3-12

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

The wing of an aircraft can be considered as a cantilever beam of length L, as shown in the Figure below. If the airlift is approximated as a sinusoidally distributed load, TEX y q(x)=q, sin- L find the displacement of the tip A. Consider only bending. The bending rigidity is El, uniform. s L q=qosin(x/L) A X
2. Solve the following problem of bars in axial load using the finite element method, finding a) displacements at the nodes, b) reactions at supports, c) forces and stresses in each element. Consider E1=E2=E3=200GPa, A1= 20x10-4 m2, A2= 10x10-4 m2, A3= 8x10-4 m2 for the bars. F2= 40kN, F3= 50kN
A differential element on the bracket is subjected to plane strain that has the following components: , strain at x = 250 x 10-6, strain at y = 300 x 10-6, strain at x y= -500 x 10-6. Use the strain-transformation equations and determine the normal strain strain x' in the x' direction on an element oriented at an angle of 35°. Note, a positive angle is counter clockwise.
An element in uniaxial stress is subjected totensile stresses σx = 57 MPa, as shown in the figure.Using Mohr’s circle, determine the following.(a) The stresses acting on an element oriented at anangle θ =-33° from the x axis (minus meansclockwise).(b) The maximum shear stresses and associatednormal stresses.Show all results on sketches of properly orientedelements.
Gate AB in Figure is hinged at A, has width b into the paper, and makes smooth contact at B. The gate has density ps and uniform thickness t. For what gate density ps, expressed as a function of (h, t, p, 0), will the gate just begin to lift off the botton B
Determine by integration the centroid (?̅) of theshape in the figure (to the right).
Problem: For the beam and loading shown, determine (a) the equation of the elastic curve, and (b) the deflection midway between the supports. Assume that EI is constant for the beam. You can use any method for the beam deflection computation. w(x) = w,x/L³ Wo %3D A B
A beam having the cross section shown is subjected to a vertical shear V. Determine (a) the horizontal line along which the shearing stress is maximum, (b) the constant k in the following expression for the maximum shearing stress.τmax=k*V/Awhere A is the cross-sectional area of the beam
16 Yield point is the boundary in the stress-s train diagram where stress loses its prop ortionality with strain.( 17 True 18 False Strain is the ratio deformation over origin al length.( True False The value of stress can be unitless. True False
QUESTION 1 An axial bar is shown below. E = 200 × 10⁹ Pa, A = 0.42 × 10-³ m². The bar can be divided into two elements. Using the finite element method, determine (a) the nodal displacements (b) the strain and strain energy of element 2 (c) the support reactions of the bar Element 1 0.4 m 2 Element 2 70 kN 0.5 m 3
An element in plane stress is subjected to stresses σ_x, σ_y, and τ_xy (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle θ from the x axis. Show these stresses on a sketch of an element oriented at the angle θ. (Note: The angle θ is positive when counterclockwise and negative when clockwise.) Given: σ_x=33 MPa,σ_y=-9 MPa,τ_xy=29 MPa,θ=35°