(exism an X 150 mm y X F=80kN A e=40 mm 350 mm X- y Le=40 mm X

For the cantilever beam shown in the figure below, invoke the equilibrium of cut free-body sections of the beam to (a) write equations for the shear force and bending moment distributions as functions of x. Include a free-body diagram of each cut section and force and moment balance calculations. Examine the shear force and bending moment formulas and deduce the sign of the deformation within each inter- val. Include a sketch of a deformed material element that illustrates the shear and bending deformation within the interval. (b) Find the shear force of the largest magnitude in the beam and state where it occurs within the beam. (c) Find the bending moment of the largest magnitude in the beam and state where it occurs within the beam. 200 N/m 0.6 m- X 600 N 0.2 m 0.2 m

4. The box beam is made of an elastic-perfectly plastic material for which the yield 250 MPa. Draw the residual stress distribution in the beam after the elastic-plastic moment, Mep = 548.5 kNm, is applied and then released. It can be shown that under the applied moment, the flanges (260 mm × 30 mm) yield, while the webs (2 x 200mm x 30mm) show linear elastic behavior. The moment of inertia and plastic section modulus of the section are given below: I = 247.48 x 106 mm4; Z, = 2394000 mm³ stress oy = y 30 mm 30 mm 200 mm 200 mm 30 mm 30 mm

The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 40.4 ksi. Assume P = 51 kips, L1=6.6 ft, and L2=19.8 ft.   (a) Determine the minimum section modulus required for this beam.   (b) From the table below, select the lightest W shape that can be used for this beam.   (c) What is the total weight of the steel beam itself (i.e., not including the loads that are carried by the beam)?