A simply supported beam has a solid rectangular cross-section and is subjected to loading as shown in Figure 2. Knowing that the modulus of elasticity of the beam is 200 GPa and neglecting the weight of the beam, determine:
1. The reaction forces at supports A and C.
2. Use Macaulay's method to calculate the slope at point B and the deflection at the midspan of the beam.
3. If the cross-section of the beam is replaced by a hollow rectangular beam with a thickness of mm and unchanged dimensions, explain the slope at point B and the deflection at the midspan of the beam. Also, determine which beam is better to support the corresponding loads.
[31.32 kN, 16.18 kN, -0.08 rad, -62.1 mm]
20 kN
15 kN
25 kN
60 mm
0.3 m
0.2 m
0.5 m
0.5 m
0.3 m
40 mm
Figure 2