Question

If the beam has a concentrated load acting on it in the center of the beam, then the deflection must satisfy the symbolic boundary value problem: $frac{d^4y}{dx^4} = -Fdelta(x-a)$, where $x = a$ is the point where the mass is applied, $F$ is the force applied and the minus sign indicates that the force is downward. The end points of the beam satisfy the conditions, y(0) = 0, y''(0) = 0, y(L) = 0, y''(L) = 0. Problem 3. Suppose that length of the beam is 4m, and suppose that $EI = 1$. Further suppose that the force $F = 2$ is applied at $x = 3$. Then, we $y(x)$ satisfies the symbolic boundary value problem $frac{d^4y}{dx^4} = -2delta(x - 3)$, y(0) = 0, y(4) = 0 y''(0) = 0, y''(4) = 0. Use the technique of the Laplace transform to determine the vertical deflection y(x). (Hint: Let y'(0) = A and y'''(0) = B. Use the formula $L{y^{(n)}}(s) = s^nY(s) - s^{n-1}y(0) - s^{n-2}y'(0) - ... - y^{(n-1)}(0)$ for n = 4 to solve for the Laplace transform Y(s) of y(x) and then use the conditions y(4) = y''(4) = 0 to find A and B.)

          If the beam has a concentrated load acting on it in the center of the beam, then the deflection must satisfy the
symbolic boundary value problem:
$frac{d^4y}{dx^4} = -Fdelta(x-a)$,
where $x = a$ is the point where the mass is applied, $F$ is the force applied and the minus sign indicates that
the force is downward. The end points of the beam satisfy the conditions,
y(0) = 0,  y''(0) = 0,
y(L) = 0,  y''(L) = 0.
Problem 3. Suppose that length of the beam is 4m, and suppose that $EI = 1$. Further suppose that the force
$F = 2$ is applied at $x = 3$. Then, we $y(x)$ satisfies the symbolic boundary value problem
$frac{d^4y}{dx^4} = -2delta(x - 3)$,
y(0) = 0, y(4) = 0  y''(0) = 0, y''(4) = 0.
Use the technique of the Laplace transform to determine the vertical deflection y(x). (Hint: Let y'(0) = A and
y'''(0) = B. Use the formula $L{y^{(n)}}(s) = s^nY(s) - s^{n-1}y(0) - s^{n-2}y'(0) - ... - y^{(n-1)}(0)$ for n = 4 to solve for
the Laplace transform Y(s) of y(x) and then use the conditions y(4) = y''(4) = 0 to find A and B.)

$If the beam has a concentrated load acting on it in the center of the beam, then the deflection must satisfy the symbolic boundary value problem: fracd^4ydx^4 = -Fdelta(x-a), where x = a is the point where the mass is applied, F is the force applied and the minus sign indicates that the force is downward. The end points of the beam satisfy the conditions, y(0) = 0, y”(0) = 0, y(L) = 0, y”(L) = 0. Problem 3. Suppose that length of the beam is 4m, and suppose that EI = 1. Further suppose that the force F = 2 is applied at x = 3. Then, we y(x) satisfies the symbolic boundary value problem fracd^4ydx^4 = -2delta(x - 3), y(0) = 0, y(4) = 0 y”(0) = 0, y”(4) = 0. Use the technique of the Laplace transform to determine the vertical deflection y(x). (Hint: Let y'(0) = A and y”'(0) = B. Use the formula Ly^(n)(s) = s^nY(s) - s^n-1y(0) - s^n-2y'(0) - ... - y^(n-1)(0) for n = 4 to solve for the Laplace transform Y(s) of y(x) and then use the conditions y(4) = y”(4) = 0 to find A and B.)$

Added by Brandy R.

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