Choosing an Appropriate Section Determine the axial forces in members DG and BE of the truss in Fig. 6.23. Strategy An appropriate choice of section is not obvious, and it isn't clear beforehand that we can determine the requested information by the method of sections. We can't obtain a section

Question

Choosing an Appropriate Section

Determine the axial forces in members DG and BE of the truss in Fig. 6.23.

Strategy

An appropriate choice of section is not obvious, and it isn't clear beforehand that we can determine the requested information by the method of sections. We can't obtain a section that involves cutting members DG and BE without cutting more than three members. However, cutting members DG, BE, CD, and BC results in a section with which we can determine the axial forces in members DG and BE even though the resulting free-body diagram is statically indeterminate.

Accepted Answer

etermine the Reactions at the Supports We draw the free-body diagram of the entire truss in Fig. a. From the equilibrium equations,

[latex]\sum{F_{x} } = A_{x} = 0[/latex],

[latex]\sum{F_{y} } = A_{y} + K - F - 2F - F= 0[/latex],

[latex]\sum{M_{(point A)} } = -FL - 2F(2L) - F(3L) + K(4L) = 0[/latex],

we obtain the reactions [latex] A_{x} = 0 , A_{y} = 2F , and K = 2F.[/latex]

Choose a Section In Fig. b, we obtain a section by cutting members DG, CD, BC, and BE. Because the lines of action of [latex] T_{BE} , T_{BC}, T_{CD}[/latex] pass through point B, we can determine [latex] T_{DG}[/latex] by summing moments about B:

[latex]\sum{M_{(point B)} } = -2FL - T_{DG}(2L) = 0 .[/latex]

The axial force [latex] T_{DG} = -F.[/latex] Then from the equilibrium equation

[latex] F_{x} = T_{DG} + T_{BE} = 0,[/latex]

we see that [latex] T_{BE} = -T_{DG} = F. [/latex] ember DG is in compression, and member BE is in tension.

Question 6.5: Choosing an Appropriate Section Determine the axial forces i...

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