A Pratt steel truss is to be designed to support three loads 1 R , 2 R and 1 R a

Question

A Pratt steel truss is to be designed to support three loads 1 R , 2 R and 1 R as shown. The length of the truss is L ? 2L1 ? 2L2 . The height of the truss and thus the angle ? , as well as the crosssectional

areas of the various members, are to be selected to obtain the most economical design. Specifically, the cross-sectional area of each member is chosen so that the stress (force divided

by area) in that member is equal to (i) c ? if the member is in compression or (ii) t ? if the member is in tension, where c ? and t ? are the allowable stress values in the material of the

member. This is done to minimize the total weight, and thus the total cost, of the truss.

*=degrees

For this problem, assume R1=13.3kN(weight of a compact car) R2=24.1kNand (weight of an SUV) with L1= 5m and L2= 7m. and . Take 10*<O<85* . Ignore the weight of any zero-force members in your computations.

a) Derive the analytical expression for the force in every member of the truss in terms of , , , , and ; 1 R 2 R 1 L 2 L(b

) Assume the truss

material is steel with a specific gravity (weight per unit volume) of

77 kN/m and allowable stress values of t c ? ?? ?125 MPa . Plot the volume of each loadbearing

member with respect to ? in one graph. Also, plot the total weight of the truss with

respect to ? ;

(c) In the given range of ? , which individual members are the heaviest for the steel truss? [Hint:

At different ? values, there may be different heaviest members];

(d) Now, assume the truss material is fiber-reinforced plastic (FRP) with a specific gravity of

3 17 kN/m and allowable stress values of t ? ? 50 MPa and c ? ?190 MPa . Plot the volume

of each load-bearing member with respect to ? in one graph. Also, plot the total weight of

the truss with respect to ? ;

(e) In the given range of ? , which individual members are the heaviest for the FRP truss?

(f) Obtain the optimum value of ? and the corresponding weight of the truss for the steel truss

and FRP truss from Parts (b) and (d). Which material is better? Explain.

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