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## Q. p.24.1

The beam shown in Fig. P.24.1 is simply supported at each end and carries a load of 6000 N. If all direct stresses are resisted by the flanges and stiffeners and the web panels are effective only in shear, calculate the distribution of axial load in the flange ABC and the stiffener BE and the shear flows in the panels.

## Verified Solution

From the overall equilibrium of the beam in Fig. S.24.1(a)
$R_{\mathrm{F}}=4 \mathrm{kN} \quad R_{\mathrm{D}}=2 \mathrm{kN}$
The shear load in the panel ABEF is therefore 4 kN and the shear flow q is given by

$q_1=\frac{4 \times 10^3}{1000}=4 \mathrm{~N} / \mathrm{mm}$

Similarly

$q_2=\frac{2 \times 10^3}{1000}=2 \mathrm{~N} / \mathrm{mm}$

Considering the vertical equilibrium of the length h of the stiffener BE in Fig. S.24.1(b)

$P_{\mathrm{EB}}+\left(q_1+q_2\right) h=6 \times 10^3$

where $P_{\mathrm{EB}}$ is the tensile load in the stiffener at the height h, i.e.
$P_{\mathrm{EB}}=6 \times 10^3-6 h$ (i)
Then from Eq. (i), when h = 0, $P_{\mathrm{EB}}$ = 6000 N and when h = 1000 mm. $P_{\mathrm{EB}}$ = 0. Therefore the stiffener load varies linearly from zero at B to 6000 N at E.

Consider now the length z of the beam in Fig. S.24.1(c). Taking moments about the bottom flange at the section z

$P_{\mathrm{AB}} \times 1000+R_{\mathrm{F}} z=0$
whence
$P_{\mathrm{AB}}$ = −4z N
Thus $P_{\mathrm{AB}}$ varies linearly from zero at A to 4000 N (compression) at B. Similarly $P_{\mathrm{CB}}$ varies linearly from zero at C to 4000 N (compression) at B.