The simply supported beam shown in FIGURE 1

The simply supported beam shown in FIGURE 1 is 10 m long with
E = 200 × 109 Pa and I = 150 × 10–6 m4.

As it won't let me upload the image, I'll try to explain it. R1 and R2 are at either end of the supported beam and the u.d.l is 5kNm-1. Three metres from R1 (on the left hand side) is a point load of 20kN. Four metres from this is a point load of 30kN and then a further three metres before point R2 (at the far right).

(a) (i) Determine the position and magnitude of the maximum bending
moment.
(ii) Plot a graph of the deflection along the length of the beam
(calculate the deflection at 1 m intervals).
(b) What I value for the beam would be required to halve the maximum
deflection of the beam ?
(c) The calculation for the maximum bending moment is to be verified
experimentally using a strain gauge bonded to the outer surface of the
beam, at the point where the maximum bending moment occurs.
Derive an equation which could be used to calculate the bending
moment from the measured strain v