2 For the loading shown, determine (a) the equation of the elastic curve for the cantilever beam (b) AB, the deflection at the free end, (c) the slope at the free end. Figure 1 The deflection curve for a simple beam AB is given by the following equation determine the reactions RA and RB at the supports. Determine the maximum bending moment Mmax. Figure 2 3. The distributed load acting on a cantilever beam has an intensity given by the expression AB q q0cos(πx/2L), where is the maximum intensity of the load (see figure 3). q0 Derive the equation of the deflection and then determine the deflection at the free end. Use the fourth δB order differential equation of the deflection curve (the load equation). Figure 4. Beam hangs from two springs, as shown in the figure. The springs have stiffnesses and and the ACB k1 k2 beam has flexural rigidity EI. What is the downward displacement of point which is at the midpoint of the beam, when the load is C, P applied? Data for the structure are as follows: kN, m, kN∙m2, kN/m, and kN/m. P=8.0 L=1.8 EI=216 k1=250 k2=160 Figure
2 For the loading shown, determine (a) the equation of the elastic curve for the cantilever beam AB, (b) the deflection at the free end, (c) the slope at the free end. Figure 1 The deflection curve for a simple beam AB is given by the following equation determine the reactions RA and RB at the supports. Determine the maximum bending moment Mmax. Figure 2 3. The distributed load acting on a cantilever beam AB has an intensity q given by the expression q0cos(πx/2L), where q0 is the maximum intensity of the load (see figure 3). Derive the equation of the deflection and then determine the deflection δB at the free end. Use the fourth order differential equation of the deflection curve (the load equation). Figure 4. Beam ACB hangs from two springs, as shown in the figure. The springs have stiffnesses k1 and k2 and the beam has flexural rigidity EI. What is the downward displacement of point C, which is at the midpoint of the beam, when the load P is applied? Data for the structure are as follows: P=8.0 kN, L=1.8 m, EI=216 kN∙m2, k1=250 kN/m, and k2=160 kN/m. Figure