elastic curve

Deflection of Cantilever Beams | Area-Moment Method

General representation of deflection of catilever beams

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.

 

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

630 Overhang beam with point load at free end

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.)

 

Solution to Problem 621 | Double Integration Method

621 Overhang beam at both ends with uniform load over its entire span

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.)

 

Solution to Problem 620 | Double Integration Method

620 Beam loaded with symmetrical triangular load

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.)

 

Solution to Problem 619 | Double Integration Method

619 Overhang beam with moment and uniform loads

Problem 619

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

 

Solution to Problem 618 | Double Integration Method

618 Simply supported beam carrying a couple

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 (link inactive for a moment).

 

Solution to Problem 614 | Double Integration Method

614 Overhang beam with point load at the end of overhang

Problem 614

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

 

Solution to Problem 608 | Double Integration Method

608 Cantilever Beam Loaded with Triangular Load

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.

 

Solution to Problem 607 | Double Integration Method

607 Cantilever Beam with Point Load

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.

 

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