Consider a propped cantilever beam of length L loaded with a uniformly distributed load (UDL) of w = 0.5 T/m over its entire span. If the beam is fixed at one end and simply supported at the other, find the maximum positive shear force in the beam.

Determine the slope at point A (θA) for a simply supported beam with flexural rigidity EI under an asymmetric load condition.

Calculate the maximum tension in a cable having supports at the same level with a span of 15 m and a maximum dip of 3 m. The cable is subjected to a uniformly distributed load of 20 kN/m throughout its span and point loads of 60 kN and 20 kN at the middle third points.