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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 629 | Moment Diagrams by Parts

Problem 629
Solve Prob. 628 if the sense of the couple is counterclockwise instead of clockwise as shown in Fig. P-628.
 

Simple beam loaded with triangular and moment loads

 

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Solution to Problem 628 | Moment Diagrams by Parts

Problem 628
For the beam loaded with uniformly varying load and a couple as shown in Fig. P-628 compute the moment of area of the M diagrams between the reactions about both the left and the right reaction.
 

Simple beam loaded with triangular and moment loads

 

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Solution to Problem 627 | Moment Diagram by Parts

Problem 627
For the beam loaded as shown in Fig. P-627compute the moment of area of the M diagrams between the reactions about both the left and the right reaction. (Hint: Resolve the trapezoidal loading into a uniformly distributed load and a uniformly varying load.)
 

627-uniformly-varying.gif

 

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Solution to Problem 626 | Moment Diagram by Parts

Problem 626
For the beam loaded as shown in Fig. P-626, compute the moment of area of the M diagrams between the reactions about both the left and the right reaction.
 

Simple beam with uniform load over the middle span

 

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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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Area-Moment Method | Beam Deflections

Another method of determining the slopes and deflections in beams is the area-moment method, which involves the area of the moment diagram.
 

Deviation and Slope of Beam by Area-Moment Method

 

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Moment Diagram by Parts

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.
 

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Solution to Problem 621 | Double Integration Method

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.)
 

621-given-figure.jpg

 

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