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

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.

p.21.4
Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

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

\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}

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

\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}

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

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

26.6\times10^{3}\times550=59.2\times225\times500+29.6\times250\times225+2\times500\times225q_{s,0}

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

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
s.21.4.a
s.21.4.b
s.21.4.c

Related Answered Questions