Write shear and moment equations for the beams in the following problems. In each problem, let x be the distance measured from left end of the beam. Also, draw shear and moment diagrams, specifying values at all change of loading positions and at points of zero shear. Neglect the mass of the beam in each problem.

For the beam shown derive the reaction forces, moments, slope and deflection curves using the method of integration. Use E, and I for the modulus of Elasticity and Inertia, respectively. wo A

A simply supported beam carries a moment applied to one end as shown. El is constant. a) Calculate the support reaction forces for the beam b) Write out the M(x) equation using discontinuity functions. c) Determine the slope and deflection equations by integrating the M(x) equation as needed and using two B.C. to solve for the integration constants, C1 and C2. d) Calculate the deflection at the mid-span of the beam. e) Check: Calculate the deflection at point B (right support). A 12A

For the beam and loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the beam, (b) the location of the maximum deflection, and (c) the maximum beam deflection. Assume that El is constant for the beam. Let w = 11 kN/m, L = 4.5 m, E = 190 GPa, and I = 145 x 106 mm4. B L Answer: (b) x = (c) Vmax mm

Please help me with solution to Item 4 (Sub question No- 4) For the beam below: Draw the approximate deflected shape from the bending moment diagram. Develop the piecewise functions of θ(x) and v(x) using double integration. Assume EI is constant. Take x to be references from the farthest left point on the beam If w = 2 k/ft and L = 5 ft, locate the point of maximum deflection between supports A and B. Develop a variable based excel program that allows you to plot both the slope and displacement functions with x.  In other words, your program should be able to take any value of w, L, E, I and x and automatically calculate deflection and slope.  Print x-y scatter plots connected by smooth lines for both the deflection and slope using values of x ranging from 0 to 2L in increments of 0.5 ft.  Plot the displacement in inches and slope in radians for the following cases using your program: i) w = 2 k/ft, L = 5 ft, E = 4,176,000 ksf, I = 0.073784 ft4 ii) w = 10 k/ft, L = 6 ft, E =…

1-) Calculate the deflection and slope of the C point of the elastic curve for the loading condition given in the figure. Find it using the method of integration. 2-)For the loading case given in the figure, use the deflection and slope method of the point C for the moment Find it using.

Solve the problem by the moment-area method. The beam has constant flexural rigidity EI. A simple beam AB supports two concentrated loads P at the positions shown in the figure. B C 4. 4 A support C at the midpoint of the beam is positioned at distance d below the beam before the loads are applied. Assuming that d = 12 mm, L = 5.4 m, E = 200 GPa, and I = 193 x 10° mm, calculate the magnitude of the loads P (in kN) so that the beam just touches the support at C. 163.87 x kN

For the loading shown, use the double-integration method to determine (a) the equation of the elastic curve for the cantilever beam, (b) the deflection at the free end, and (c) the slope at the free end. Assume that El is constant for the beam. Let wo = 7 kN/m, L = 5.0 m, E = 185 GPa, and I = 110x 10° mm4. B L Answer: (b) VA = mm (c) ĐA = rad

Two Dimensional Force System Let the force (F) shown below with the direction (0); we can resolve this force into two components: 1-Horizontal Component (Fx) which lies on X-axis. 2-Vertical Cor nent (Fy) which lies on Y-axis. y F Leca R

Obtain the shear (V), moment (M) and deflection (Δ) diagrams and the equations that define them.