elastic curve

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

 

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

 

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

 

Solution to Problem 620 | Double Integration Method

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.)
 

Beam loaded with symmetrical triangular load

 

Solution to Problem 619 | Double Integration Method

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

Overhang beam with moment and uniform loads

 

Solution to Problem 618 | Double Integration Method

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.
 

Simply supported beam carrying a couple

 

Solution to Problem 614 | Double Integration Method

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

Overhang beam with point at the end of overhang

 

Solution to Problem 608 | Double Integration Method

Problem 608
Find the equation of the elastic curve for the cantilever beam shown in Fig. P-608; it carries a load that varies from zero at the wall to wo at the free end. Take the origin at the wall.
 

Cantilever Beam Loaded with Triangular Load

 

Solution to Problem 607 | Double Integration Method

Problem 607
Determine the maximum value of EIy for the cantilever beam loaded as shown in Fig. P-607. Take the origin at the wall.
 

Cantilever Beam with Point Load

 

Solution to Problem 606 | Double Integration Method

Problem 606
Determine the maximum deflection δ in a simply supported beam of length L carrying a uniformly distributed load of intensity wo applied over its entire length.
 

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