For the multi-web, multi-stringer open-section beam shown, determine

- (a) the shear flow distribution,
- (b) the location of the shear center.

EQUATION USED

SOLUTION

The location of the centroid with respect to stringer 4, and moments of inertia are

(a) With no horizontal shear force, and with the above information, equation A14.14 reduces to

Starting at stringer 1 and working around to stinger 6, the shear flow due to the vertical shear is

The shear flow diagram and the location and direction of each force component for this section are shown below.

It is important to pay attention to the location of each force, especially the ones for the semicircular webs.

(b) To determine the 'x' coordinate of the shear center the web forces need to be calculated. Then the moments are summed about stringer 4 with clockwise positive.

To find the 'y' coordinate of the shear center, a fictitious horizontal shear force 'Vx' is applied to the beam, then the same analysis is repeated.

Now calculate the force in each web.

Use the moment equilibrium to determine the y-coordinate of the shear center.

The shear center location is shown in the figure below.

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