30 k 10 ft 10 ft V (k) M (k-ft) У

Determine/derive the Shear and Moment Equations of each segment of the beam (kindly include the FBD). Compute the Reactions and Draw the detailed Shear and Moment Diagram indicating values.

For the beam and loading shown use the double-integration method the equation of the elastic curve for segment AB of the beam, (b) the deflection midway between A and B, and (c) the slope at B. Assume that El is constant for the beam. to determine (a) L.

Start with the shear diagram. To use a segment of the left end of the beam to develop the expression for the shear, the vertical reaction at A must be known. Calculate the vertical reaction at A. Let a positive force act up.   Write an expression for the internal shear for an arbitrary point between A and B.   Write an expression for the internal shear for an arbitrary point between B and C.   Draw the shear diagram for the beam.   Write an expression for the bending moment at an arbitrary point between A and B. Use the standard sign convention for the internal moment for a beam.   Write an expression for the bending moment at an arbitrary point between B and C.   Draw the moment diagram for the beam.

For the beam below, determine the displacement at x = 2L/3 from the fixed support using the deflection tables provided in the FE equation packet. Take EI as a constant. Indicate the direction of the displacement also.

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

Using the virtual work method determine slope of the beam at "A". Beam is subjected to a uniformly Distributed Load “W" and a concentrated moment "WL^2" at “A" (Express the results in terms of W, L, and EI) w ikIft=constant)

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

PROBLEM # 3: Use the conjugate beam method and determine the slope at B and the displacement at C of the beam. "EI" is constant. 2 A В a a a a

Problem 2: For the beam given below: (a) Calculate all support reactions. (b) Draw the shear diagram. Show all important values of shear. Show the sign convention within each region. (c) Draw the moment diagram. Show all important values of moment. Show the sign conventions within each region (concavity: smiley face, sad face, etc.) (d) Sketch the deflected shape. Show supports in your sketch. For your solution, let w = 2 kips/ft and L = 20 ft. A L 22 B L W C