Chapter 15, Problem 51RP

For the beam and loading shown, determine the equations of the shear and bending-moment curves and the maximum absolute value of the bending moment in the beam, knowing that (a) k= 1, (b) k= 0.5.

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.

Determine the distance a for which the maximum absolute value of the bending moment in beam AB is as small as possible.

Draw the shear and bending moment diagrams for the beam and loadin g shown, and determine the maximum absolute value ( a ) of the shear, ( b ) of the bendin g moment.

Two small channel sections DF and EH have been welded to the uniform beam AB of weight W = 3 kN to form the rigid structural member shown. This member is being lifted by two cables attached at D and E . Knowing that 0= 30° and neglecting the weight of the channel sections, (a) draw the shear and bending-moment diagrams for beam AB, (b) determine the maximum absolute values of the shear and bending moment in the beam.

For the beam and loading shown, determine the maximum absolute values of the shear and bending moment

For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the location and magnitude of the maximum absolute value of the bending moment.

A cable AB of span L and a simple beam A'B' of the same span are subjected to identical vertical loadings as shown. Show that the magnitude of the bending moment at a point C' in the beam is equal to the product T0h,  where T0 is the magnitude of the horizontal component of the tension force in the cable and h is the vertical distance between point C and the chord joining the points of support A and B.

Determine (a) the distance a for which the maximum absolute value of the bending moment in the beam is as small as possible, (b) the corresponding maximum normal stress due to bending.