Sign conventions for Shear force and Bending Moment diagrams

Always consider arbitrary sections for drawing shear force and bending moment diagrams.

Shear force: Force acting in right hand side of the section in upward direction is taken as negative and force in right hand side of the section acting in downward direction is taken as positive. Similarly, a force in left hand side of the section is taken positive, if it is acting in upward direction direction and it is taken as negative if it is acting in downward direction. Not getting anything then look at the picture given below.

Bending Moment: First of all remove all loads and reactions from any one side of the section. now introduce each load and reaction one at a time and find its effect at the section. A bending moment causing concavity upwards is taken positive and called as sagging bending moment. A bending moment which is causing convexity upwards (or concavity downwards) is taken negative and called as hogging bending moment.

In general the moment due to every downward force is negative and the moment due to every upward force is positive.

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