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Someone please help me with this problems.. A beam, subject (to a triangular loa

ID: 1858305 • Letter: S

Question

Someone please help me with this problems..

A beam, subject (to a triangular load as* shown in the figure is supported at the left) end by a single force P and is anchored in the wall at its right end. Ultimate objective of this homework problem is to find the force I such that the left and right end of the beam are at the same level y=0. As such this problem is statically indeterminate and the beam is called a constrained beam The triangular load is such that its weight per running meter is zero at the wall and equal to w0 Newtons per running meter at x=a. Your data : Total length: L-3.6[m] Distance : a - 0.6 m] Load characteristics : w0 = 150 [N/m] Modulus of elasticity : E- 200 [MPa] Central moment of inertia : I - 12000 [cm4] Required accuracy) for numerical results: +/-!% percent \ hat arc the correct boundary conditions for this ease ? Choose one option each for i=0 and i=L, respectively : There are two principly different ways to solve this problem. One way is to derive the equation for the deflection curve by the method of integration with he support force P as variable. The appearing integration constants and the force P can be determined from the boundary conditions, I encourage you to try this route the second way, which you must follow in order to answer the questions below is the following. You first determine the deflection curve for the beam for the triangular load and the force P (with P as variable) separately and request that the deflections at x=0 for these two cases are equal but of opposite sign. This gives you a single equation for the force P. The advantage of this way is that the two individual load scenarios can be solved each either by the method of integration or by the method of superposition. Consider the shown beam deflection due to the triangular load only What are the correct boundary conditions for this case ? Choose one option each for x=0 and x=L respectively : Now determine the deflection curve for the triangular load (try both the method of integration and the method of superposition) and determine the deflection and the angle of deflection at x=0. (Enter positive values for both quantities) : Deflection [cm]: Angle of deflection [rad) ! From (tie equation for the deflection of a beam due to a single force P with the above boundary conditions détermine the force P by requiring that the deflection due lo the force P and due to the triangular load have to sum up to zero. What is the value of the force P [N] ? What would be the angle of deflection at x=0 due to this force P alone [rad] (enter a positive value) ? What is the angle of deflection at x=O due to the combined action of force P and the triangular load (rad) (enter a positive value) ?

Explanation / Answer

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