elastic curve

Problem 664
The middle half of the beam shown in Fig. P-664 has a moment of inertia 1.5 times that of the rest of the beam. Find the midspan deflection. (Hint: Convert the M diagram into an M/EI diagram.)
 

Problem 663
Determine the maximum deflection of the beam carrying a uniformly distributed load over the middle portion, as shown in Fig. P-663. Check your answer by letting 2b = L.
 

Problem 662
Determine the maximum deflection of the beam shown in Fig. P-662. Check your result by letting a = L/2 and comparing with case 8 in Table 6-2. Also, use your result to check the answer to Prob. 653.
 

Problem 661
Compute the midspan deflection of the symmetrically loaded beam shown in Fig. P-661. Check your answer by letting a = L/2 and comparing with the answer to Problem 609.
 

Problem 660
A simply supported beam is loaded by a couple M at its right end, as shown in Fig. P-660. Show that the maximum deflection occurs at x = 0.577L.
 

Problem 659
A simple beam supports a concentrated load placed anywhere on the span, as shown in Fig. P-659. Measuring x from A, show that the maximum deflection occurs at x = √[(L² - b²)/3].
 

Problem 658
For the beam shown in Fig. P-658, find the value of EIδ at the point of application of the couple.
 

Problem 657
Determine the midspan value of EIδ for the beam shown in Fig. P-657.
 

Problem 656
Find the value of EIδ at the point of application of the 200 N·m couple in Fig. P-656.
 

Generally, the tangential deviation t is not equal to the beam deflection. In cantilever beams, however, the tangent drawn to the elastic curve at the wall is horizontal and coincidence therefore with the neutral axis of the beam. The tangential deviation in this case is equal to the deflection of the beam as shown below.