Refer to the truss depicted below to complete each problem. The figure is associated with Problems $6-59/60$ in Structural Analysis, ${11}^{th}$ edition by Hibbeler. The truss is supported by a pin at A and a roller at $E.$ Consider the following set of design loads:

a concentrated live load of $1000$ lb $,$

a uniformly distributed live load of $250l\frac{b}{f}t,$ and

a uniformly distributed dead load of $125l\frac{b}{f}t.$

Also assume that the loads act along the bottom chord of the truss, from $A$ to $E.$

Problem $1.$ Construct the influence line for the force in member $GH$ and determine the maximum member force. If the influence line for member $GH$ contains both positive and negative ordinate values, then position the live loads so as to produce the maximum positive and negative values.

Problem $2.$ Construct the influence line for the force in member $CH$ and determine the maximum member force. If the influence line for member $CH$ contains both positive and negative ordinate values, then position the live loads so as to produce the maximum positive and negative values.

Problem $3.$ Construct the influence line for the force in member $DE$ and determine the maximum member force. If the influence line for member $DE$ contains both positive and negative ordinate values, then position the live loads so as to produce the maximum positive and negative values.