Determine the shear-force and bending-moment distributions in the beam

For the beam and loadings shown, a) Use dicontinuity functions to write the expression for the expression for w(x); include the beam reactions in this expression. b) Integrate w(x) twice to determine V(x) and M(x). c) Use V(x) and M(x) to plot the shear force and bending moment diagrams.

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

Calculate the internal shear force and the internal bending moment for the beam at every point x, and sketch the shear and moment diagrams. At what point in the beam (x=?) does the maximum normal stress occur?  Find the maximum normal stress, 0 , due to bending, At what point in the cross section (y=?) does the maximum normal tensile stress occur?? Find the magnitude of the maximum transverse shear stress on the cross section, T, due to bending at the point “A”. At what point in the cross section (y=?) does the maximum transverse shear stress occur?