The North bond of an interstate freeway is in need of a beam

The North bond of an interstate freeway is in need of a beam structure to support a relatively Large rectangular road sign The sign made of Aluminum is 10 ft long, 6 ft tall and 1 inch thick. You are asked to design a horizontal beam, which will be welded to a left vertical column and hinged to a right vertical column. The span of the beam (the distance between the two vertical supporting columns) is given as 50ft. The sign will be placed and welded on top of the beam. The left edge of the sign needs to be 20ft away from the left support on the beam. The effect of wind in the area is insignificant. As a designer, you are constrained to only use the beam cross section shown in the figure. Design the beam so that it can survive the bending stress and shear stress. Calculate the deflection of your beam.

Solution

ia is reqs. Unless you give the dimensions of the beam it will be impossible to evaluate your choces.

The beam is a T beam, for which the Moment of inertia is reqd. ssume you know it as I

The important parameters to consider are: The wt of the sign, and the moment at the left support which is welded.

The wt of the sign is W, for 10*6*1/12 cft = 5 cft of Al which weighs 250 lb/ft3 approx, so 1250 lb total

If this is considered to act at the centre, which is 25 ft away from the left corner, you have a moment of 1250*25 ft lb acting there = 31250 ftlb.

There could be buckling of the left support, and bending st ress due to the moment = 31250.c/I where c/I is the neurtral axis/moment of inertia of the T beam. Taking a value of 40000 psi for limiting stress of Al, c/I needs to be less than 40/31.25 = 1.28

Put in a safety factor of 2 for limit stress, get c/I = .64, so C needs to be reduced and I increased in some way.

The shear stress is Reaction/area of the bear. reaction on left would be approx 625 lb, shear stress can be determined and must be less than the limit for Al, fond to be 50 Kps