Chapter A14 Sample Test

TRANSVERSE SHEAR IN OPEN SECTIONS
SAMPLE TEST

1. A vertical shear force of 35,000 N is applied at the shear center of the beam section shown. Determine

(a) the shear flow diagram (magnitude and direction),
(b) the maximum shear stress and its location,
(c) the coordinates of the shear center (ex and ey), measured from the middle of the vertical web.

(a) the shear flow values at points 1 through 7 are:

(b) max. shear stress = 50.92 MPa, occurs in horizontal webs near points 3 and 5.
(c) ex = 48.57 mm (to the left of vertical web), ey = 0 (due to horizontal symmetry)

2. For the beam section shown below having a vertical centroidal moment of inertia of 2.515 in4 and under a horizontal transverse shear force of 2,515 lb through the shear center,

(a) determine and sketch the shear flow pattern with all values well defined.
(b) Determine the value of maximum shear stress and its location.
(c) Determine the vertical position of the shear center measured from the web centerline.

(b) max. shear stress = 38.98 psi, it occurs at the junction of the horizontal web and 4-in vertical flange.
(c) ey = .3022 in above horizontal web.

3. For the constant shear flow section shown, determine

(a) the magnitude of the resultant shear force,
(b) the location of the resultant shear force,
(c) the direction of the resultant shear force.

The resultant shear force is in the direction from A to B.

4. For the open-section beam shown, determine the location of the shear center (i.e., ex and ey).
Assume the webs are ineffective in supporting bending.

5. For the open-section beam shown, determine the location of the shear center (i.e., ex and ey) measured from stringer a.

ex = 19.3 in, to the right of a
ey = 18.5 in, below a.