Determine the vertical displacement of joint A. The truss is made from A992 steel rods having a diameter of 30 mm.

Question

Determine the vertical displacement of joint A.The truss is made from A992 steel rods having a diameter of 30 mm.

Accepted Answer

Members Real Force N. As indicated in Fig. a .
Members Virtual Force n. As indicated in Fig. b.
Virtual Work Equation. Since [latex]\sigma_{\max }=\frac{F_{B D}}{A}=\frac{50\left(10^{3} ight)}{\frac{\pi}{4}\left(0.03^{2} ight)}=70.74 MPa <\sigma_{Y}=345 MPa,[/latex]

member	n(N)	N(N)	L(m)	nNL([latex]N^{2}.m[/latex])
AB	-0.75	[latex]-15(1^{3})[/latex]	3	33.75([latex]10^{3})[/latex]
AD	1.25	[latex]25(10^{3})[/latex]	2.5	78.125([latex]10^{3}[/latex])
BC	1	[latex]40(10^{3})[/latex]	2	80([latex]10^{3}[/latex])
BD	-1.25	[latex]-50(10^{3})[/latex]	2.5	156.25([latex]10^{3}[/latex])
CD	1.5	[latex]45(10^{3})[/latex]	1.5	101.25([latex]10^{3}[/latex])
				[latex] \sum 449.375(10^{3})[/latex]

Then

[latex]1 \cdot \Delta=\Sigma \frac{n N L}{A E} \1 N \cdot\left(\Delta_{A} ight)_{v}=\frac{449.375\left(10^{3} ight)}{\frac{\pi}{4}\left(0.03^{2} ight)\left[200\left(10^{9} ight) ight]} \\left(\Delta_{A} ight)_{v}=3.179\left(10^{-3} ight) m =3.18 mm \downarrow[/latex]

Question 14.83: Determine the vertical displacement of joint A. The truss is...

Related Answered Questions

member	n(N)	N(N)	L(m)	nNL( $N^{2}.m$ )
AB	-0.75	$-15(1^{3})$	3	33.75( $10^{3})$
AD	1.25	$25(10^{3})$	2.5	78.125( $10^{3}$ )
BC	1	$40(10^{3})$	2	80( $10^{3}$ )
BD	-1.25	$-50(10^{3})$	2.5	156.25( $10^{3}$ )
CD	1.5	$45(10^{3})$	1.5	101.25( $10^{3}$ )
				$\sum 449.375(10^{3})$