Determine the largest force that can be developed in member BC of the bridge truss shown in Fig. 6–26a due to a moving force of 20 k and a moving distributed load of 0.6 k/ft.The loading is applied at the top cord.

Question

Determine the largest force that can be developed in member [latex]B C[/latex] of the bridge truss shown in Fig. [latex]6-26 (\mathrm{a})[/latex] due to a moving force of [latex]20 \mathrm{k}[/latex] and a moving distributed load of [latex]0.6 \mathrm{k} / \mathrm{ft}[/latex]. The loading is applied at the top cord.

Accepted Answer

Tabulate Values. A table of unit-load position [latex]x[/latex] at the joints along the top cord versus the force in member [latex]B C[/latex] is shown in Fig. 6-26b. The method of sections can be used for the calculations. For example, when the unit load is at joint [latex]I(x=20 \mathrm{ft})[/latex], Fig. 6-26a, the reaction [latex]\mathbf{E}_{y}[/latex] is determined first [latex]\left(E_{y}=0.25\right)[/latex]. Then the truss is sectioned through [latex]B C, H B[/latex], and [latex]H I[/latex], and the right segment is isolated, Fig. 6-26c. One obtains [latex]\mathbf{F}_{B C}[/latex] by summing moments about point [latex]H[/latex] to eliminate [latex]\mathbf{F}_{H I}[/latex] and [latex]\mathbf{F}_{H B}[/latex]. In a similar manner determine the other values in Fig. 6-26b.

Influence Line. A plot of the tabular values yields the influence line, Fig. 6-26d. By inspection, [latex]B C[/latex] is a primary member. Why?

Concentrated Live Force. The largest force in member [latex]B C[/latex] occurs when the moving force of [latex]20 \mathrm{k}[/latex] is placed at [latex]x=40 \mathrm{ft}[/latex]. Thus,

[latex] F_{B C}=(1.33)(20)=26.7 \mathrm{k} [/latex]

Distributed Live Load. The uniform live load must be placed over the entire deck of the truss to create the largest tensile force in [latex]B C[/latex].* Thus,

[latex] F_{B C}=\left[\frac{1}{2}(80)(1.33)\right] 0.6=32.0 \mathrm{k} [/latex]

Total Maximum Force

[latex] \left(F_{B C}\right)_{\max }=26.7 \mathrm{k}+32.0 \mathrm{k}=58.7 \mathrm{k} [/latex]

*The largest tensile force in member [latex]G B[/latex] of Example 6-15 is created when the distributed load acts on the deck of the truss from [latex]x=0[/latex] to [latex]x=8 \mathrm{~m}[/latex], Fig. 6-24d.

Question 6.17: Determine the largest force that can be developed in member ...

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