In construction, engineers must deploy support beams to counter-balance weights. For example, imagine a beam, say 10 meters long, that's stretched from one end of a building frame to another with a support beam on both ends. Next, imagine two or more weights or loads are placed on that beam putting downward pressure on the support beams. Engineers must properly size the support beams to handle the weights.

Equal and Symetrical Weights

Find the weight of the two equal and symmetrical weights pressing downward on a beam in units kilograms or "kg." Call the first weight F1 and the second weight F2. With symmetrical weights, F1 is equal to F2 and each weight is located equal distance from the support beam. Refer to the construction drawings for the building framework design.

Calculate the size of the support beam for F1 using the formula R1 = [(F1 * a) + (F2 * a)]/2 where "R1" is the support beam for F1 and "a" is the acceleration of gravity at 9.82 meters/seconds squared. As an example, assume both F1 and F2 is 300 kilograms:

R1 = [(300)(9.82) + (300)(9.82)]/2 = (2946 + 2946)/2 = 2,946 Newtons. This indicates how much force the support beam, R1, has to withstand.

Calculate the size of the support beam for F2 using the formula R2 = [(F1 * a) + (F2 * a)]/2 where R2 is the support beam for F2. It's the same formula as R1 since F1 is equal to F2:

R2 = [(300)(9.82) + (300)(9.82)]/2 = (2946 + 2946)/2 = 2,946 Newtons.

Non-Equal and Non-Symetrical loads

Find the total length of the beam that stretches from one end to the other. Refer to the construction drawings for the building framework design. Call this value TL. As an example, assume TL is 12 meters.

Find the weight of F1 and the distance it is located from R1. Refer to the construction drawings for the building framework design. Call this distance L1. As a example, assume F1 is 400 kg and L1 is 2 meters.

Find the weight of F2 and the distance it is also located from R1. Refer to the construction drawings for the building framework design. Call this distance L2. As an example, assume F2 is 600 kg and L2 is 3 meters.

Calculate the balance force, or "BF," using the formula BF = [(F1 * a) + (F2 * a)]. Using the example numbers:

BF = [(400)(9.82) + (600)(9.82)] = 3,928 + 5,892 = 9,820 newtons.

Calculate the size of the support beam for R2 using the formula R2 = [(F1 * a * L1) + (F2 * a * L2)]/TL. Continuing with the example numbers:

R2 = [(400)(9.82)(2) + (600)(9.82)(3)]/12 = [7, 856 + 17,676]/12 = 25,532/12 = 2,127 newtons.

Calculate the size of the support beam R1 using the formula R1 = BF - R2. Continuing with the example numbers:

R1 = 9,820 - 2,127 = 7,693 newtons.