For the cantilever beam shown determine the normal and shear

For the cantilever beam shown, determine the normal and shear stresses acting at point K. The cross-sectional dimensions of the beam cross section and the location of point K are also shown. Use the following values: a = 2.15 m, b = 0.80 m, Py = 15 kN, Pz-5 kN, bf = 160 mm, k = 47 mm, tf= 13 mm, h = 43 mm, tw-7 mm, and d = 239 mm. (a P. Calculate the cross-sectional area, the moment of inertia about the z centroidal axis, and the moment of inertia about the y centroidal axis for the cross-section Answers:

Solution

Bending stress at K due to M_y :

Rotate the crossection by 90 degrees clockwise about positive X-axis.

Let K be at a distance of l₁ from neutral axis.

l₁ = 0.5 * (b_f - (k + t_w + k))= 0.5 * (160-(47 + 7 + 47))= 29.5 mm

From Flexural Formula,

Bending stress = M_y * l₁ / I_y = - 10.75 * 10³ * 29.5 * 10^-3 / (8.88 * 10⁶ * 10^-12) = -35.71 MPa

It is compressive in nature.