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Problem 1 (35 points). yf L q=q(x) F=3P X L=12; P=7; q(x) = Px(x-L) 1. State mathematical formulation of the problem (balance equation and boundary conditions) (3 points) 2. Determine the type of boundary conditions (essential or natural) (2 points) 3. Solve the problem by Galerkin method using $\eta_1 = N_1 = x$, $\eta_2 = N_2 = x^2$ (26 points). 4. Compute the residual $r_y$ of the boundary condition specified at x=L (2 points). 5. Determine the residual in balance equation, $r_o$. (2 points) Solution MUST CONTAIN all necessary formulas, equations and all intermediate results.

          Problem 1 (35 points).
yf
L
q=q(x)
F=3P
X
L=12;
P=7;
q(x) = Px(x-L)
1. State mathematical formulation of the problem (balance equation and boundary
conditions) (3 points)
2. Determine the type of boundary conditions (essential or natural) (2 points)
3. Solve the problem by Galerkin method using $\eta_1 = N_1 = x$, $\eta_2 = N_2 = x^2$ (26
points).
4. Compute the residual $r_y$ of the boundary condition specified at x=L (2 points).
5. Determine the residual in balance equation, $r_o$. (2 points)
Solution MUST CONTAIN all necessary formulas, equations and all intermediate results.

Show more…

Problem 1 (35 points).
yf
L
q=q(x)
F=3P
X
L=12;
P=7;
q(x) = Px(x-L)
1. State mathematical formulation of the problem (balance equation and boundary
conditions) (3 points)
2. Determine the type of boundary conditions (essential or natural) (2 points)
3. Solve the problem by Galerkin method using η1 = N1 = x, η2 = N2 = x^2 (26
points).
4. Compute the residual ry of the boundary condition specified at x=L (2 points).
5. Determine the residual in balance equation, ro. (2 points)
Solution MUST CONTAIN all necessary formulas, equations and all intermediate results.

Added by Steven B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Karan Soni

Step 1

The distributed load is given by q(x) = Px(x - L). The balance equation for the beam, assuming it is simply supported or cantilevered, would typically be the beam's differential equation of bending, which is derived from the equilibrium of moments and forces. Show more…

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Problem 1 (35 points): Given: F = 3P X = 7 L = 12 P = 7 q(x) = Px(x - L) 1. State the mathematical formulation of the problem (balance equation and boundary conditions) (3 points). 2. Determine the type of boundary conditions (essential or natural) (2 points). 3. Solve the problem by the Galerkin method using n = N = x, n = N = x (26 points). 4. Compute the residual r of the boundary condition specified at x = L (2 points). 5. Determine the residual in the balance equation (0.2 points). Solution MUST CONTAIN all necessary formulas, equations, and all intermediate results.

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