Simple Beam Loads

Concentrated Load

A concentrated load is an idealized simplification of a load whose extent is very small compared to the length of the beam. For example, if a mass m is hung by a rope and the rope is tied around a long beam at some location x=A along the beam, then the load is well-approximated by a concentrated force of magnitude mg (where g is the acceleration due to the earth's gravity).

One of the simulations in the interactive portion of this lab is the bending of a cantilevered beam (i.e. a beam clamped at one end as pictured below) with a concentrated load placed at x=L (the end of the beam.)

Uniform Load

A uniform load is a load that exerts equal force along each point of the beam's length. If the total mass of the load is m , then the force per unit length that the beam feels is q (x ) = q0 where q0 = mg /L

Triangular Loads

A triangular load is a load whose force varies linearly along the beam's length and which is zero at one of the beam's ends. If the total mass of the load is m , then the force that the beam feels at x is q (x ) = q0 (1-x/L ) for a "left-handed" triangular load or q (x ) = q0 x/L for a "right-handed" triangular load where q0 = 2mg/L .

Parabolic Loads

A parabolic load is a load whose force varies quadratically along the beam's length and which is zero at one of the beam's ends. For the purpose of this lab, we assume that if the total mass of the load is m , then the force that the beam feels at x is q (x ) = q0 (1- (x/L )^²) for a "left-handed" parabolic load or q (x ) = q0 (1- (x/L-1 )^²) for a "right-handed" parabolic load where q0 = 3mg/ (2L ).

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The Geometry Center Calculus Development Team