Question

Chapter 6- Influence Lines Draw the influence line for the shear and moment at C for the beam shown below. The support at A is a roller and the support at B is a pin. The beam is subjected to a uniform load of 5 kip/ft over its entire length and a single 12 kip concentrated force. Deternmine the maximum values of Ve and Mc and the position of the applied concentrated force for each condition. Answer: VC: +0.5 at left, 0 at A,-0.5 at CL, +0.5 at CR, o at B,-0.25 at right; concentrated load at left end or just to the right of C Vmx 15.375 k Mc: -5 ft at left, O at A, +5 ft at C, at B, -2.5 ft at right; concentrated load at C MC-max = +1 53.75 k-ft. 5 ft 10 ft-m 10 ft

Answer 1

Using Muller�s breaslva�s Principe. V_c max = + 1/2 (0.5) (10) (5) - 1/2 (0.5) (10) (5) + 1/2 (0.5) (10) (5) - 1/2 (0.25) (5) (5) V_c max = + 15.375 kip rightarrow Place concentrated load @ just right of 'c� M_c max: = -1/2 (10) (5) (5) + 1/2 (20) (5) (5) + 12 (5) - 1/2 (2.5) (5) (5) M_c max = + 153.75 kip-ft Place concentrated load @ c