3. Use the conjugate-beam method to determine the slopes at ends A and D and the deflections at points B and C of the beam shown in Figure. El is constant. ㅏ -20 ft- 60 k B 40 k C 10-10- El constant E- 1,800 ksi I= 46,000 in 4

Rigid bar ABC is supported by bronze rod (1) and stainless steel rod (2) as shown in the figure. A concentrated load of P = 22 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 70°F. Use the following dimensions and properties: a = 3.5 ft, b = 7.3 ft. Rod (1): d₁1.10 in., L₁ = 13ft, E₁ = 15,200 ksi, a₁ = 12.20 x 10-6/°F. Rod (2): d₂ = 0.70 in., L₂ = 9ft, E₂ = 28,000 ksi, %₂ = 9.60 x 10-6/°F. = 6ft, E3 = 15,200 ksi, a3 = 12.20 x 10-6/°F. Rod (3): d = 1.15 in., L VD = i (1) (2) a b H Rigid bar B (3) L3 OD L in. N P L₂

Civil Engineering An overhanging beam is loaded as shown below. Calculate the deflections under the two loads 80KN and the slope at D in terms of El using Macaulay's method. El is constant. 80KN 120KN 80KN A + 2m 5m 3m D 2m Figure 1

Rigid bar ABC is supported by bronze rod (1) and stainless steel rod (2) as shown in the figure. A concentrated load of P = 16 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 125°F. Use the following dimensions and properties: a = 2.8 ft, b = 6.3 ft. Rod (1): d₁ = 0.90 in., L₁ = 11 ft, E₁ = 15,200 ksi, α₁ = 12.20 × 10-6/°F. Rod (2): d₂ = 0.80 in., L₂ = 9 ft, E2 = 28,000 ksi, a₂ = 9.60 × 10-6/F. Rod (3): d3 = 1.25 in., L3 = 5 ft, E3 = 15,200 ksi, a3 = 12.20 x 10-6/°F. VD = i L in. (1) A a L3 B (3) D b Rigid bar L2