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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

 

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Solution to Problem 655 | Deflections in Simply Supported Beams

Problem 655
Find the value of EIδ under each concentrated load of the beam shown in Fig. P-655.
 

Simple Beam with Two Concentrated Loads

 

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Solution to Problem 641 | Deflection of Cantilever Beams

Problem 641
For the cantilever beam shown in Fig. P-641, what will cause zero deflection at A?
 

Unknown point force P and counterclockwise moment in cantilever beam

 

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Solution to Problem 640 | Deflection of Cantilever Beams

Problem 640
Compute the value of δ at the concentrated load in Prob. 639. Is the deflection upward downward?
 

Cantilever beam with uniform downward load and concentrated upward load

 

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Solution to Problem 636 | Deflection of Cantilever Beams

Problem 636
The cantilever beam shown in Fig. P-636 has a rectangular cross-section 50 mm wide by h mm high. Find the height h if the maximum deflection is not to exceed 10 mm. Use E = 10 GPa.
 

Cantilever beam with two concentrated loads

 

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Solution to Problem 632 | Moment Diagrams by Parts

Problem 632
For the beam loaded as shown in Fig. P-632, compute the value of (AreaAB) barred(X)A. From this result, is the tangent drawn to the elastic curve at B directed up or down to the right? (Hint: Refer to the deviation equations and rules of sign.)
 

Overhang beam with point and rectangular loads

 

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Solution to Problem 630 | Moment Diagrams by Parts

Problem 630
For the beam loaded as shown in Fig. P-630, compute the value of (AreaAB)barred(X)A . From the result determine whether the tangent drawn to the elastic curve at B slopes up or down to the right. (Hint: Refer to the deviation equations and rules of sign.)
 

Overhang beam with point load at free end

 

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Solution to Problem 625 | Moment Diagram by Parts

Problem 625
For the beam loaded as shown in Fig. P-625, compute the moment of area of the M diagrams between the reactions about both the left and the right reaction. (Hint: Draw the moment diagram by parts from right to left.)
 

Uniform load over 3/4 of span and concentrated load at midspan of simple beam

 

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Solution to Problem 624 | Moment Diagram by Parts

Problem 624
For the beam loaded as shown in Fig. P-624, compute the moment of area of the M diagrams between the reactions about both the left and the right reaction.
 

Simple beam with moment and point loads

 

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