Statics

Pages

Bending Moment in a Beam

 , where:

M = Bending Moment (N*m)

E = Young's Modulus (Pa)

I = Area Moment of Inertia (m^4)

w = Deflection (m)

x = Length (m)

Bulk Modulus

 , where:

K = Bulk Modulus (Pa)

V = Volume (m3)

P = Pressure (Pa)

Critical Buckling Force

Maximum theoretical force before buckling

 , where:

F = Critical Force Before Buckling (N)

E = Young's Modulus (Pa)

I = Area Moment of Inertia (m^4)

L = Length of Column (m)

Curvature

 , where:

K = Curvature (1/m)

 = Slope

x = Length (m)

w = Deflection (m)

 = Radius of Curvature

Deflection of a Beam with a Point Load

The deflection of a beam with a point load is given by the equation below.  Note that the point need not be at the end, the beam (which is assumed to have no mass) deflects by the same amount irrespective of its actual length.

w(x) = \tfrac{Px^2(3L-x)}{6EI} , where:

Pages