Step 5 -- Calculate the deflection in four segments

Input := 

y1[x_] = 0 + Integrate[yp1[u], {u,0,x}];
y2[x_] = y1[30] + Integrate[yp2[u], {u,30,x}];
y3[x_] = y2[60] + Integrate[yp3[u], {u,60,x}];
y4[x_] = y3[100] + Integrate[yp4[u], {u,100,x}];