In structural mechanics, the moment-area method is a semi-graphical technique for determining slope and deflection of beams that relies on the bending-moment diagram divided by the flexural rigidity (EI, the product of the material's modulus of elasticity and the cross-section's moment of inertia about the neutral axis), termed the M/EI diagram. It is governed by two theorems: the first states that the change in slope between two points on a beam's elastic curve equals the area of the M/EI diagram between those points, derived from the differential relation between curvature and bending moment (1/ρ = M/EI); the second states that the tangential deviation of one point from the tangent line drawn at another point equals the first moment (about the point of deviation) of the M/EI diagram area between them. The method extends the differential-equation approach to elastic-curve analysis and applies equally to beams of non-uniform (variable) moment of inertia, where the M/EI diagram's ordinates vary with local flexural rigidity.
In structural mechanics, the moment-area method is a semi-graphical technique for determining slope and deflection of beams that relies on the bending-moment diagram divided by the flexural rigidity …