Beam equations are an essential part of mechanics and a great way to hone your math and physics skills. The ability to calculate forces acting on beams is a fundamental in construction, scientific education and even basic home improvement, such as building shelves.
Beam equations also allow you to work out unknown things, such as how much a box weighs or how long a beam is, by rearranging the equations. This is a way to save time and effort if you need to known the weight of a fixed object without the hassle of dismantling whatever it is fixed to.
Draw a diagram including the forces acting on the beam and the length of the beam. This helps to visualize the problem and allows you to collect all the supplied information together in one picture. This is often called a free-body diagram in textbooks.
Use a scale to determine the clockwise force acting on the beam (if present), measured in Newtons (N). If the force is to the left of the balancing point, then acting upwards (lifting) causes a clockwise moment. If acting on the right of the balancing point then a downward force (gravity) causes a clockwise moment. Label the Clockwise Force "Fc."
Use a ruler to measure the horizontal distance in meters (m) between the clockwise force and the center of the balancing point, if present. Label this distance "dc."
Use a scale to determine the anticlockwise force, measured in Newtons (N) acting on the beam, if present. If the force is to the left of the balancing point, acting downwards (gravity) causes an anti-clockwise moment. If acting on the right of the balancing point, an upward force (lifting) causes an anticlockwise moment. Label the clockwise force "Fa."
Use a ruler to measure the horizontal distance in meters (m) between the anticlockwise force and the center of balance point, if present. Label this distance "da." By now one unknown should have arisen: "Fc," "dc," "Fa" or "da."
Calculate the clockwise moments (Mc) by using the formula for a moment:
Mc = Fc x dc.
A clockwise moment is equal to the clockwise force multiplied by the horizontal distance from the balancing point.
Calculate the anticlockwise moments (Ma) by using the formula for a moment:
Ma = Fa x da.
An anticlockwise moment is equal to the anticlockwise force multiplied by the horizontal distance from the balancing point.
Let the clockwise moments equal the anticlockwise moments to find the values when they are in balance:
Fa x da = Fc x dc
This is known in physics as equilibrium.
Make the unknown force or distance the subject of investigation by rearranging the formula to isolate the unknown on one side of the equation. This is done by dividing the other side of the equation by the known force or distance.
For example, if we want to find dc, divide the equation by Fc:
dc = (Fa x da) / Fc
Input the known numbers into the equation and solve the equation for the unknown. The solved equation gives the force or distance required to balance the two sides of the beam.
The answer must be equal to or greater than this number if we want to lift the object.
One kilogram (Kg) is equal to 9.81 Newtons (N). If the weight of an object is given in kilograms, it must be multiplied by 9.81 to give the force in Newtons before a calculation can be made.