Hinge

FIGURE 3.71 Beams and corresponding conjugate beams for various types of supports.

FIGURE 3.72 Deflection calculations for a cantilever by the conjugate beam method.

(a) Cantilever beam with a load on the end.

(b) Bending-moment diagram. (c) Conjugate beam loaded with M/EI distribution. (d) Deflection at B equals the bending moment at B due to the M/EI loading.

FIGURE 3.72 Deflection calculations for a cantilever by the conjugate beam method.

(a) Cantilever beam with a load on the end.

(b) Bending-moment diagram. (c) Conjugate beam loaded with M/EI distribution. (d) Deflection at B equals the bending moment at B due to the M/EI loading.

3.33.2 Moment-Area Method

Similar to the conjugate-beam method, the moment-area method is based on Eqs. (3.130a) to (3.130d). It expresses the deviation in the slope and tangential deflection between points A and B on a deflected beam:

Equation (3.131a) indicates that the change in slope of the elastic curve of a beam between any two points equals the area under the M/EI diagram between these points. Similarly, Eq. (3.131b) indicates that the tangential deviation of any point on the elastic curve with respect to the tangent to the elastic curve at a second point equals the moment of the area under the M/EI diagram between the two points taken about the first point.

For example, deflection SB and rotation dB at point B in the cantilever shown in Fig. 3.72a are f3L/4 M(x) ,

Renewable Energy 101

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