Consider the following statements:

A simply supported beam is subjected to a couple somewhere in the span. It would produce
(i) A rectangular SF diagram.
(ii) Parabolic BM diagrams.
(iii) Both +ve and -ve BMs which are maximum at the point of application of the couple. 
Of these statements

Concept:

• SFD is 1° higher than the loading curve and BMD is 1° higher than the SF curve.

• If S.F. changes sign at a section then B.M at that section is either maximum or minimum.

• If BM changes sign at a point, then such a point is called a point of contraflexure or inflection. If BM changes sign curvature also changes.

• The rate of change of BM is equal to SF at that section or the slope of BM curve represents SF at that point.

• The negative slope of SF curve at a point represents the downward loading rate.

• If at a point concentrated load or reaction is present, then at that point ordinate of the SF curve will change suddenly and the slope of BM curve will also change.

• If at a point Concentrated moment or couple is present then ordinate of the BM curve will change suddenly.

• If over a span a constant SF is present only then such span is called shear span.

• If over a span BM is constant and SF = 0, then such a span is in pure bending and under pure bending the deflected shape will be an arc of a circle.

Additional Information

• A couple is a system of two equal and opposite forces whose lines of action do not coincide.

• The two forces create a rotational effect (moment) without causing any net translation of the body.

• The effect of a couple is to rotate the body around its center of mass or a fixed point.