The moment-area method of finding the deflection of a beam will demand the accurate computation of the area of a moment diagram, as well as the moment of such area about any axis. To pave its way, this section will deal on how to draw moment diagram by parts and to calculate the moment of such diagrams about a specified axis.
 

Problem 621
Determine the value of EIδ midway between the supports for the beam shown in Fig. P-621. Check your result by letting a = 0 and comparing with Prob. 606. (Apply the hint given in Prob. 620.)
 

Problem 620
Find the midspan deflection δ for the beam shown in Fig. P-620, carrying two triangularly distributed loads. (Hint: For convenience, select the origin of the axes at the midspan position of the elastic curve.)
 

Problem 619
Determine the value of EIy midway between the supports for the beam loaded as shown in Fig. P-619.
 

Problem 618
A simply supported beam carries a couple M applied as shown in Fig. P-618. Determine the equation of the elastic curve and the deflection at the point of application of the couple. Then letting a = L and a = 0, compare your solution of the elastic curve with cases 11 and 12 in the Summary of Beam Loadings.
 

Problem 617
Replace the load P in Prob. 616 by a clockwise couple M applied at the right end and determine the slope and deflection at the right end.
 

Problem 616
For the beam loaded as shown in Fig. P-616, determine (a) the deflection and slope under the load P and (b) the maximum deflection between the supports.
 

Problem 615
Compute the value of EI y at the right end of the overhanging beam shown in Fig. P-615.
 

Problem 614
For the beam loaded as shown in Fig. P-614, calculate the slope of the elastic curve over the right support.
 

Problem 613
If E = 29 × 10⁶ psi, what value of I is required to limit the midspan deflection to 1/360 of the span for the beam in Fig. P-613?