1. Evaluate the bending moment at a given section Make this evaluation in terms
ID: 1822311 • Letter: 1
Question
1. Evaluate the bending moment at a given section
Make this evaluation in terms of the distance x from the left-hand support to this section.
Thus RL = N/L; M = NxIL.
2. Write the differential equation of the elastic curve;
integrate twice
Thus Elcfy/dx2 = -M = -Nx/L; Eldyldx = EIS = -Nx2/(2L) + C1; Ely = -Nx3/(6L) + C1X +
C2.
3. Evaluate, the constants of integration
Apply the following boundary conditions: When x = O, y = O; /. C2 = O; when x = L, y = O;
/.C1 =NL/6.
4. Write the slope and deflection equations
Substitute the constant values found in step 3 in the equations developed in step 2. Thus
O = [N/(6EIL)](L2 - 3*2); y = [Nx/(6EIL)](L2 - x2).
5. Find the slope at the supports
Substitute the values x = O, x = L in the slope equation to determine the slope at the supports.
Thus S1 = NL/(6EI); SR = -NL/(3EI).
6. Solve for the section of maximum deflection
Set 6 = O and solve for ;c to locate the section of maximum deflection. Thus L2 - 3x2 = O;
x = L/3°5. Substituting in the deflection equation gives ymsai = M,2/(9£/3°5).
Explanation / Answer
Torque, moment of a force T, (M) T = r ~ F N m Energy E J Potential energy Ep, V, ƒ³ Ep = . ç F . ds J Kinetic energy Ek, T, K Ek = (1/2)mv2 J Work W, w W = ç F . ds J Hamilton function H H (q, p) J = T(q, p) + V(q) Lagrange function L L (q, qE) J = T(q, qE) . V(q)
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