Static Analysis Af A Beam Do Fe Static Analysis Of A Two Span Beam Shown In The Figure N P1 0 P1 P2 P2 12 Q 2 1 V 1 (203.09 KiB) Viewed 46 times
Static analysis af a beam Do FE static analysis of a two-span beam shown in the figure. N P1 = 0 P1 P2 P2 = -12 q.2 1) voor Me P3 = q.L P4 = 0 E E 8I E, I P5 = 4 q.L? L L X X P6 = 0 w The known data are: E- Young's modulus of the beam material, I - moment of inertia of the cross-section, L- length, q- distributed load (in units of force per length). In the general case, the beam is subjected to the load of: - P2 and P3 forces (positive values correspond to the positive displacement w), - M2 and M3 bending moments (positive clockwise), - distributed loads with constant values of p1 and P2 (positive values as in the case of forces).
1) discretise the geometry of the beam with two beam elements: (three nodes 1,®,3; element nr 1 connects the nodes Di ; element nr 2 connects Ⓡ i 3) 2) provide the stiffness matrices k of finite elements and vectors of nodal forces equivalent to continuous loading 3) build the global stiffness matrix K of the structure under consideration 4) write the components of the load vector Facting on the structure 5) specify the boundary conditions 6) calculate the displacements and angles of rotation at nodes 1,2,3 7) determine the reactions 8) verify the equilibrium of the structure 9) using shape functions calculate the displacement W4 and the angle of rotation 04 at the point 4 (corresponding to x=L) 8) sketch the beam deflection and the rotation angles 9) calculate the internal forces (M, T) in both elements and based on them sketch the variation of bending moments and transverse forces in the beam
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