If the vertical plane of symmetry in the beam of P.21.3 is swept back by 25° as shown in plan in Fig. P.21.4, the span of 3 m is retained and the 40 kN load is applied as in P.21.3, calculate the flange and stringer loads and the shear flow distribution at a section 1.5 m from the built-in end.

Question

Accepted Answer

As in S.21.3 and referring to Figs. P.21.4, S.21.4(a), and S.21.4(b),

[latex]\begin{aligned}& P_{z, 1}=-P_{z, 2}=-133300 N \&P_{z, 3}=P_{z, 5}=-P_{z, 4}=-P_{z, 6}=-66650N\end{aligned}[/latex]

The solution now continues in Table S.21.4.
From Table S.21.4,

[latex]\begin{aligned}& \sum\limits_{r=1}^n P_{x, r}=0,\sum\limits_{r=1}^n P_{y, r}=13.4 kN \& \sum\limits_{r=1}^nP_{x, r} \eta_r=28.2 kNm , \sum\limits_{r=1}^nP_{y, r} \xi_r=0\end{aligned}[/latex]

Then [latex]S_{x,w}=0,\,S_{y,w}=40-13.4=26.6\,\mathrm{kN}[/latex]

The [latex]q_{\mathrm{b}}[/latex] shear flows are the same as in S.21.3, so taking moments about boom 2,

[latex]26.6 imes10^{3} imes550=59.2 imes225 imes500+29.6 imes250 imes225+2 imes500 imes225q_{s,0}[/latex]

from which [latex]q_{s,0}=27.6\ \mathrm{N/mm.}[/latex]

The final shear flows are then as shown in Fig.S.21.4(c).

Table S.21.4
Boom	$\begin{aligned}& P z, r \\& (k N)\end{aligned}$	$\delta x_r / \delta z$	$\delta y_r / \delta z$	$\begin{gathered}P _{ x , r } \\( k N )\end{gathered}$	$\begin{gathered}P _{ y , r } \\( k N )\end{gathered}$	$\underset{( k N )}{ P _{ r }}$	$\begin{gathered}\xi_r \\( mm )\end{gathered}$	$\begin{gathered}\eta _{ r } \\( m m )\end{gathered}$	$\begin{aligned}& P _{x, r} \eta_r \\& ( kNm )\end{aligned}$	$\begin{aligned}& P_{y, r} \xi_r \\& ( kNm )\end{aligned}$
1	-133.3	0.47	–0.025	–62.7	3.3	–147.3	250	112.5	7.05	–0.83
2	133.3	0.47	0.025	62.7	3.3	147.3	250	112.5	7.05	0.83
3	-66.7	0.47	–0.025	–31.3	1.7	–73.7	0	112.5	3.52	0
4	66.7	0.47	0.025	31.3	1.7	73.7	0	112.5	3.52	0
5	-66.7	0.47	–0.025	–31.3	1.7	–73.7	250	112.5	3.52	–0.42
6	66.7	0.47	0.025	31.3	1.7	73.7	250	112.5	3.52	0.42

Question 21.4: If the vertical plane of symmetry in the beam of P.21.3 is s......

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