The governing differential equation for the deflection of a cantilever beam subjected to a point load...

 

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The governing differential equation for the deflection of a cantilever beam subjected to a point load at its free end (Fig. 1) is given by: d?y Elzz dx2 -Px where E is elastic modulus, I, is beam moment of inertia, y is beam deflection, P is the point load, and x is the distance along the beam measured from the free end. The boundary conditions are the deflection y(L) is zero and the slope (dy/dx) at x=L is zero, where L is beam length. Solve for the deflection of the beam using the shooting method. Use L=2 m, I,= 0.0005 m*, P- 10 kN, and E= 200,000 MPa. Provide a plot comparing your results against the analytical solution given by: P (L – x)² (2L + x) 6E12 у (х) %3 Constant Elz Ay A B →X L. PV Fig. 1. Cantilever beam subjected to a concentrated load (P) at its free end. The governing differential equation for the deflection of a cantilever beam subjected to a point load at its free end (Fig. 1) is given by: d?y Elzz dx2 -Px where E is elastic modulus, I, is beam moment of inertia, y is beam deflection, P is the point load, and x is the distance along the beam measured from the free end. The boundary conditions are the deflection y(L) is zero and the slope (dy/dx) at x=L is zero, where L is beam length. Solve for the deflection of the beam using the shooting method. Use L=2 m, I,= 0.0005 m*, P- 10 kN, and E= 200,000 MPa. Provide a plot comparing your results against the analytical solution given by: P (L – x)² (2L + x) 6E12 у (х) %3 Constant Elz Ay A B →X L. PV Fig. 1. Cantilever beam subjected to a concentrated load (P) at its free end.

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