Problem 6: Use element matrices potential energy formulations to solve the beam problem shown in Figure.5. Findnodal displacement values. Make sure to construct the grid information table and one-dimensional elements'line/mesh with appropriate labeling, numbering and displacement, loads nodal points.Steel: E = 14(105) N/cm²A = 20 cm?A = 14 cm?35500 NST=14°C20000 Na = 11(10-6)/C85 cm85-70Figure.4: Beam under axial loads

Given that, E=14×106 N/cm2δT=14 °C,α=11×10-6 /°C, Finite element equation, F1F2=AEL1-1-11u1u2For…

roblem 6: Use element matrices potential energy formulations to solve the beam problem shown in Figure.5. dal displacement values. Make sure to construct the grid information table and one-dimensional elements e/mesh with appropriate labeling, numbering and displacement, loads nodal points.

roblem 6: Use element matrices potential energy formulations to solve the beam problem shown in Figure.5. dal displacement values. Make sure to construct the grid information table and one-dimensional elements e/mesh with appropriate labeling, numbering and displacement, loads nodal points.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter10: Statically Indeterminate Beams

Section: Chapter Questions

Problem 10.4.2P: A fixed-end beam AB carries point load P acting at point C. The beam has a rectangular cross section...

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A fixed-end beam AB carries point load P acting at point C. The beam has a rectangular cross section (b = 75 mm, h = 150 mm). Calculate the reactions of the beam and the displacement at point C. Assume that E = 190 GPa.
A cantilever beam of a length L and loaded by a uniform load of intensity q has a fixed support at A and spring support at B with rotational stiffness kR. A rotation B at B results in a reaction moment MB=kRxB. Find rotation B and displacement Bat end B. Use the second-order differential equation of the deflection curve to solve for displacements at end B.
A fixed-end beam AB of a length L supports a uniform load of intensity q (see figure). Beginning with the second-order differential equation of the deflection curve (the bending-moment equation), obtain the reactions, shear forces, bending moments, slopes, and deflections of the beam. Construct the shear-force and bending-moment diagrams, Labeling all critical ordinales.
A simple beam ACE is constructed with square cross sections and a double taper (see figure). The depth of the beam at the supports is dAand at the midpoint is dc= 2d 4. Each half of the beam has length L. Thus, the depth and moment of inertia / at distance x from the left-hand end are, respectively, in which IAis the moment of inertia at end A of the beam. (These equations are valid for .x between 0 and L, that is, for the left-hand half of the beam.) Obtain equations for the slope and deflection of the left-hand half of the beam due to the uniform load. From the equations in part (a), obtain formulas for the angle of rotation 94at support A and the deflection Scat the midpoint.
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