To derive the bending moment of a simply supported beam

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DALEY BOY
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Hi I am a new member and put illustrated diagram and my answer for Ra and Re but stuggling with how to calculate the other reactions of the beam, one other thing on the illustrated diagram it show w1, w2, w3 the weight is 0.2 kg on each load case, i think this needs to be converted 0.2 x 9.81 = 1.962 . my calculations are show for moments at A and E.not sure how to draw a bending moment diagram and do calculations for B, C, D and shear force diagram would be gratfull for any help
 
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You should just scan in the actual problem, since you did not include the points "A,B,C,D,E" on your diagram, nor the value of those three weights (is it .2kg or 1.96kg ??).

Most importantly, though, you didn't write the actual problem statement and I think there is missing information. In your drawing there is a "spring load gauge," which I take to mean a spring-loaded gauge that measures deflection.

If, for example, you had this value, then this would be a sort-of frame and you could treat it as two separate bodies with equal and opposite forces at the internal hinge. Then, you could solve for the reactions (there would now be horizontal reactions), and ultimately solve for any other moment or shear that you need.