VWM - PROBLEM 4. Using the VIRTUAL WORK METHOD, and the value of El are E=200 GPa and I=18x10“ mm*. Determine the following unknowns for the prismatic cantilever beam shown below. A. The moment at the support in kN-m. B. The deflection at point B in meters. C. The deflection at point C in meters. D. The maximum deflection in meters. E. The rotation at the free-end in rad. 20 kN 30 kN/m A B D 5m 2m 2m

Consider the cantilever beam in the figure,subject to a concentrated force P = 20kip at Band a concentrated moment Mo = 100k-ft at C.Knowing that a = 5ft, use the conjugate beammethod to calculate the following in terms ofgeneric E and I:(a) The slope of point C(b)The deflection of point B

Determine the deflection at the free end A, of the simply supported beam shown in Figure 2. Use the Macaulay's method. Take EI = 5 MNm? 15 kN 15 kN 25KN/m В А 2 m 2 m 2 m 2 m Figure 2

And do g) the value of the deflection at point C in mm to three decimal points

a. Find the value of R1 for the beam loaded as shown in KN b. Find the value of R2 for the beam loaded as shown in KN c. Given the beam loaded as shown, find the value of C1 which is the first constant integration when you form the moment equation of the beam loaded as shown and integrate it once d. Determine the value of C2 when you use double integration method in determining the deflection of the beam shown

Determine the location of maximum deflection (from point A) and the value of this maximum deflection (in mm) on the simply supported beam. USE DOUBLE INTEGRATION METHOD. E=200 GPa I= 500x10^6 mm^4

A two-dimensional beam structure or frame (ABCD, shown below) has a concentrated load, P, acting on Point D. You can assume that the connections at B and C have sufficient strength to react the applied load and that loads and moments are transferred between the beams. You can assume that the members have a constant cross-section and that EI=constant.   In order to evaluate the design you must: Use any method to determine the vertical deflection at Point D. Ensure that you clearly explain your approach and show your final answer. Clearly state any assumptions made.

A beam is shown in the figure below, and the flexural stiffness of the beam section is constant El: (b) Same as above, try to find the vertical deflection of point C (Deflection).

EXAMPLE 4.3 The rod ABC is made of an aluminum for which E = 70 GPa. Knowing that P = 6 kN and Q = 42 kN, determine the deflection of (a) point A, (b) point B. 20-mm diameter 0.4 m 0,5 m 60-mm diameter