How much upward force does support 1 and support 2 exert on the beam?
How much upward force do Support 1 and Support 2 exert on the beam?
Consider a rigid beam that is 3.0 meters long and has a mass of 110 kg. It is supported at both ends. A student weighing 90 kg stands 2.0 meters away from Support 1. I would like to determine the upward forces exerted by Support 1 and Support 2 on the beam.
3 Answers
110 x 9.8 = 1078 N
90 x 9.8 = 882 N
T1 = (1078 x (3/2)) + (882 x 1) = 2499
2499 = 3T1
2499/3 = T1 = 833 N (support 1)
T2 = (1078 x (3/2)) + (882 x 2) = 3381
3381 = 3T2
3381/3 = T2 = 1127 N (support 2)
weight of beam = (110)(9.81) = 1079 N
this weight is shared (equally) by each support = 1079/2 = 539.55 N
weight of student = (90)(9.81) = 882.9 N
882.9 is shared 1/3 to 2/3 between supports 1 & 2:
support 1 => 882.9/3 = 294.3 N
support 2 => 882.9(2/3) = 588.6 N
Total Load Bearing is:
support 1 = 294.3 + 539.55 = 834 N ANS
support 2 = 588.6 + 539.55 = 1130 N ANS
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