Question

Using the equation WL^3/3EI for a simply supported aluminum beam, find the deflection. We know the beam is aluminum, it's 18.39 mm wide, 2.55 mm deep, 400 mm in total length, and a weight weighing 300 grams hangs directly in the middle of the beam. Find the aluminum beam's deflection in mm. 

          Using the equation WL^3/3EI for a simply supported aluminum beam, find the deflection. We know the beam is aluminum, it's 18.39 mm wide, 2.55 mm deep, 400 mm in total length, and a weight weighing 300 grams hangs directly in the middle of the beam. Find the aluminum beam's deflection in mm.
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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Using the equation WL^3/3EI for a simply supported aluminum beam, find the deflection. We know the beam is aluminum, it's 18.39 mm wide, 2.55 mm deep, 400 mm in total length, and a weight weighing 300 grams hangs directly in the middle of the beam. Find the aluminum beam's deflection in mm.
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Transcript

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00:01 Hi, this is the free body diagram for the given question and we have vertical force equilibrium.
00:08 So in the first part we have to calculate the vertical force equilibrium which is given by it is r a plus r b is equal to 22 plus 46 .8 plus 11 so r a will be equal to so we have so this part is r b so we have r b is equal to so summation of moment is equal to 0 which implies it is 22 into 1 .8 so 22 into 1 .8 minus r b into 3 .6 plus 46 .8 multiplied by 4 .5 plus 11 into 5 .4 is equal to 0 so we have r b is equal to it is calculated as 86 kilo newton which is acting upwards.
01:11 So we have ra given by this 22 plus 46 .8 plus 11 minus 86.
01:19 So ra will be equal to it is minus 6 .2 kiloons.
01:25 In the next part, the slope and deflection.
01:28 So slope and deflection is given by e into d square y by dx square into i.
01:37 Which is equal to m into x so m of x where m of x is the at any distance from point a so m of x from point a is given by the equation it is 46 .8 into 4 .5 minus x plus 11 into 5 .4 minus x so m of x is equal to this minus 6 .2 x minus 22 into x minus 1 .5 minus 1 .2.
02:08 Plus 80 .6 or 86 into x minus 3 .6 minus 26 by 2 into x minus 3 .6 whole square...
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