100 Mechanics of Materials §5.2 (d)Simply supported beam with central concentrated load (Fig.5.8) Fig.5.8. In order to obtain a single expression for B.M.which will apply across the complete beam in this case it is convenient to take the origin for x at the centre,then: =最-作--以坠 E少=WL、Wx2 4+A Ely -WLx2 Wx 812+Ax+B At y=0.A=0 +=⊙、x L x=2y=0 ∴.0= WL3 WL3 3296 +B WL3 B=- 48 (5.14) WL3 ymax= at the centre 48EI (5.15) and WL2 at the ends (5.16) /max =士16E1 In some cases it is not convenient to commence the integration procedure with the B.M. equation since this may be difficult to obtain.In such cases it is often more convenient to commence with the equation for the loading at the general point XX on the beam.A typical example follows:100 Mechanics of Materials $5.2 (d) Simply supported beam with central concentrated load (Fig. 5.8) W Fig. 5.8. In order to obtain a single expression for B.M. which will apply across the complete beam in this case it is convenient to take the origin for x at the centre, then: WLX2 wx3 8 12 Ely = ~-__ +Ax+B At dY x=o, -=o :. dx L 2’ x=- y=o WL3 WL3 O=- -__ +B 32 96 (5.14) 12 48 Y=- = -___ .. wL3 at the centre ymax 48EI and at the ends WLZ (5.15) (5.16) In some cases it is not convenient to commence the integration procedure with the B.M. equation since this may be difficult to obtain. In such cases it is often more convenient to commence with the equation for the loading at the general point XX on the beam. A typical example follows: