User`s guide
93
Figure 24 Neutral axis of a beam subjected to bending
Euler—Bernoulli beam theory relates curvature of a bending beam to bending moment
and rigidity of the material
where E is the elastic modulus of the material, I is the second moment of area. I must be
calculated with respect to the centroidal axis perpendicular to the applied loading. w is the
deflection in distance,
is the slope of the beam, and
equals to the beam curvature , or
.
The second moment of inertia of rectangle about the centroidal axis perpendicular to the applied
loading is expressed as
where b is the width and T is the height or thickness.
2.1.2 Calculation of Static Characteristics
Macaulay’s method (the double integration method) is a technique used in structural
analysis to determine the deflection of Euler-Bernoulli beams. Use of Macaulay’s technique is
very convenient for cases of discontinuous and/or discrete loading. Typically partial uniformly
Eq.4
Eq.5