A cantilever beam AB of length L=12 m is subjected to a concentrated load P = 35 kN and a couple Mo= 15 kN-m acting at the free end (see figure). Using Moment Area Theorems, obtain the angle of rotation and the deflection og at end B. Young's Modulus E = 200 GPa and the Moment of Inertia 1 = 105 x 10 mm. (18) JA -L- B Mo

A propped cantilever steel beam is constructedfrom a W12 x 35 section. The beam isloaded by its self-weight with intensity q. The lengthof the beam is 11.5 ft. Let E = 30,000 ksi.(a) Calculate the reactions at joints A and B.(b) Find the location of zero moment within span AB.(c) Calculate the maximum deflection of the beamand the rotation at joint B.

A cantilever beam AB, loaded by a uniform load and a concentrated load (see figure), is constructed of a channel section. 250 lb 22.5 lb/ft A 5.0 ft 3.0 ft- 0.617 in. 2.269 in. (a) Find the maximum tensile stress o, (in psi) and maximum compressive stress o, (in psi) if the cross section has the dimensions indicated and the moment of inertia about the z-axis (the neutral axis) is I = 3.10 in4. Note: The uniform load represents the weight of the beam. (Use the deformation sign convention.) O, = psi psi (b) Find the maximum value of the concentrated load (in Ib) if the maximum tensile stress cannot exceed 4 ksi and the maximum compressive stress is limited to 18.0 ksi. (Enter the magnitude.) Ib (c) How far from A (in ft) can load P = 250 lb be positioned if the maximum tensile stress cannot exceed 4 ksi and the maximum compressive stress is limited to 18.0 ksi? ft

A cantilever beam AB supports a distributed load of peak intensity g, acting over one-half of the length (see figure). (The beam has constant flexural rigidity EI. Use the second-order differential equation of the deflection curve. Enter the magnitudes.) ly 90 A C В L/2- L/2 Derive the equations of the deflection curve for the beam. (Use the following as necessary: qo, L, E, I, x.) Osxs v(x) = sxsL vx) = Also, obtain formulas for the deflections 8, and 8. at points B and C, respectively. (Use the following as necessary: 9,, L, E, I.) 7 160 E·I 11 %0 L3 192 E·I