Do i can get explained answer?
Posted: Fri May 06, 2022 6:59 am
Do i can get explained answer?
Assume that we have a tapered beam with rectangular cross-section, according to Figure 1. The beam material has a constant modulus of elasticity (Young's modulus), E and is assumed to be linear elastic. The height of the cross-section is varying linearly from x = 0 to x = L according to the function H(x) = (10L - - 9x). The beam has a constant thickness, t, and a fixed-end at point A. The beam is loaded with a constant point load P in the axial direction at point B. Assume in the following, for simplicity, that this can be regarded as a one-dimensional problem, except in problem 3 where it regarded as a 2-dimensional problem. L/3 L/3 L/3 Section C-C 10h H(x) ht 2u2 3u3 H(x=5L/6) 4u4 e1 e2 Figure 1: Axially loaded tapered beam (upper) and finite element approximation by bar elements (lower). u1 X,u H(x=L/6) C с H(x=3L/6) m 2H
Problem 1: Find an analytical expression for the displacement u(x) of the tapered beam due to the point force applied at B. The following relations are given: du(x) dx Geometric relation: € = where the one-dimensional straine is equal to the derivative of the displacement u(x) with respect to x. Constitutive relation:o = Ee, where the one-dimensional stress o is equal to the elastic modulus times the one-dimensional strain (i.e. Hooke's law). The stress is also equal to the applied axial force divided P by the cross-sectional area, o A(x)* Calculate the analytical displacements at x = x = =and x = L (i.e. put in values for x in the expression for u(x)).
- Do I Can Get Explained Answer 1 (128.5 KiB) Viewed 41 times
Problem 1: Find an analytical expression for the displacement u(x) of the tapered beam due to the point force applied at B. The following relations are given: du(x) dx Geometric relation: € = where the one-dimensional straine is equal to the derivative of the displacement u(x) with respect to x. Constitutive relation:o = Ee, where the one-dimensional stress o is equal to the elastic modulus times the one-dimensional strain (i.e. Hooke's law). The stress is also equal to the applied axial force divided P by the cross-sectional area, o A(x)* Calculate the analytical displacements at x = x = =and x = L (i.e. put in values for x in the expression for u(x)).