A simply supported beam with a cantilever side is subjected to a uniform load of 15 kN/m and a point load of 5 kN as shown in Figure 1. Assume E= 205 GPa and I=60(10)6 mm4 . (Hint: Consider method of superposition) 1.1 Calculate the reactions at the supports of the beam 1.2 Draw the shear force and bending moment diagrams with critical values 1.3 Calculate the deflection at A using unit load method

Rigid bar ABC is supported by bronze rod (1) and stainless steel rod (2) as shown in the figure. A concentrated load of P = 24 kips is applied to the free end of bronze rod (3). Determine the magnitude of the deflection of rod end D after the temperature of all rods has increased by 115 Fo. Use the following dimensions and properties: a = 3.5 ft, b = 7.5 ft. Rod (1): d 1= 1.10 in.,L 1= 12 ft , E 1= 15,200 ksi , a 1= 12.20 × 10 - 6 /Fo. Rod (2): d 2 = 0.65 in. , L 2 = 10 ft , E 2 = 28,000 ksi, a 2 = 9.60 x 10 - 6/Fo. Rod (3): d 3 = 1.15 in. , L 3 = 6 ft, E3 = 15,200 ksi , a 3 = 12.20 x 10 - 6/Fo. (1) L (2) b L2 a Rigid bar A (3) L3 vD = i in.

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

4. A beam is supported by two fixed supports and a spring as shown below. The spring constant is k = 400000 N/m. The beam is loaded by a uniform distributed load and an end moment as shown. The beam has EI = 25000 N-m². 500Nm | 1000 N/m L ↓ Im fr B 1 1 с a. Find the reactions at the three supports. b. Calculate the total deflection of the beam at point D. D COS~²³| 40.51³/