elastic curve

Solution to Problem 664 | Deflections in Simply Supported Beams

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.)
 

Simple beam with different moment of inertia over the span

 

Solution to Problem 663 | Deflections in Simply Supported Beams

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.
 

Uniform Load Over Middle Part of Simple Beam

 

Solution to Problem 662 | Deflections in Simply Supported Beams

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.
 

Simple beam with symmetrically placed uniform load

 

Solution to Problem 661 | Deflections in Simply Supported Beams

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.
 

Symmetrically Placed Point Loads over a Simple Beam

 

Solution to Problem 660 | Deflections in Simply Supported Beams

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.
 

Moment load at hinged end of simple beam

 

Solution to Problem 659 | Deflections in Simply Supported Beams

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].
 

Simple Beam with Load P at any Point

 

Solution to Problem 658 | Deflections in Simply Supported Beams

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

Simple beam loaded with counterclockwise moment

 

Solution to Problem 657 | Deflections in Simply Supported Beams

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

Simple beam under Uniformly Dereasing Load

 

Solution to Problem 656 | Deflections in Simply Supported Beams

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

Simple beam with concentrated and moment loads

 

Deflection of Cantilever Beams | Area-Moment Method

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.
 

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