Question

8. Use the Rayleigh-Ritz method to determine the deflection $v(x)$, bending moment $M(x)$, and shear force $V_y(x)$ for the beam shown in the figure. The bending moment and shear force are calculated from the deflection as: $M(x) = EI frac{d^2v}{dx^2}$ and $V_y(x) = -EI frac{d^3v}{dx^3}$. Assume the displacement as $v(x) = c_0 + c_1x + c_2x^2 + c_3x^3$, and $EI = 2,000 ext{ N} cdot ext{m}^2$, $L = 1 ext{ m}$, and $p_0 = 200 ext{ N/m}$, and $C = 100 ext{ N} cdot ext{m}$. Make sure the displacement boundary conditions are satisfied a priori. Hint: The potential energy of a couple is calculated as $V = -C frac{dv}{dx}$, where the rotation is calculated at the point of application of the couple.

          8. Use the Rayleigh-Ritz method to determine the deflection $v(x)$, bending moment $M(x)$, and shear force $V_y(x)$ for the beam shown in the figure. The bending moment and shear force are calculated from the deflection as: $M(x) = EI frac{d^2v}{dx^2}$ and $V_y(x) = -EI frac{d^3v}{dx^3}$. Assume the displacement as $v(x) = c_0 + c_1x + c_2x^2 + c_3x^3$, and $EI = 2,000 	ext{ N} cdot 	ext{m}^2$, $L = 1 	ext{ m}$, and $p_0 = 200 	ext{ N/m}$, and $C = 100 	ext{ N} cdot 	ext{m}$. Make sure the displacement boundary conditions are satisfied a priori.
Hint: The potential energy of a couple is calculated as $V = -C frac{dv}{dx}$, where the rotation is calculated at the point of application of the couple.

$8. Use the Rayleigh-Ritz method to determine the deflection v(x), bending moment M(x), and shear force Vy(x) for the beam shown in the figure. The bending moment and shear force are calculated from the deflection as: M(x) = EI fracd^2vdx^2 and Vy(x) = -EI fracd^3vdx^3. Assume the displacement as v(x) = c0 + c1x + c2x^2 + c3x^3, and EI = 2,000 ext N cdot extm^2, L = 1 ext m, and p0 = 200 ext N/m, and C = 100 ext N cdot extm. Make sure the displacement boundary conditions are satisfied a priori. Hint: The potential energy of a couple is calculated as V = -C fracdvdx, where the rotation is calculated at the point of application of the couple.$

Added by Marcos M.

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