Question

Continuing with the beam-bending topic that you have seen in prior classes and which you have reviewed recently, let q(x), V (x) and M(x) be the familiar “distributed force per unit length”, “shear force” and “bending moment”, respectively. Which of the following is correct? Explain very briefly.

Answer Choices: 1. dV dx = q and dM dx = V, or 2. dq dx = V and dV dx = M

Answer 1

For the above notation we have used in beams study, we can easily find the correct choice is the second choice as we can see in second choice is that the product of force per unit length and the length will gives us the total force acting on the beams. Here in this case the total transverse force per unit length is denoted by q(x), shear force at any section is denoted by V(x) and length at any section is denoted by x .

So q(x) * x = V(x)

Similarly,

Moment at any section is equal to the product of transverse force acting on the beam and the distance from the force to that section. Here moment at any section is denoted by M(x)

So, M(x) = q(x) * x

Also by definition we have for the above cases, we can fond the correct choices by dimension analysis.

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