At a point subjected to plane stress, the stresses are σx = 30 MPa, σy = –10 MPa, and τxy = –50 MPa. Determine the angle θp corresponding to the orientation of the principal planes at the point.

A 123-mm-long beam supports a load of P = 32 N at midspan. The cross section is rectangular with width b = 25 mm and height h = 45 mm. Determine the magnitude of the horizontal shear stress at the centroid of the cross section.

Compute φVn for the cross section shown. Assume f’c = 4,000 psi, fyt = 40,000 psi, d = 22 in., w = 16.5 in., t = 4 in., and that there are four No. 8 longitudinal tension bars and No. 3 stirrups at 6 in. o.c.

Equal shearing stresses exist on both the vertical and horizontal planes through an element.

For a beam with stirrup hooks, the free end of the bar must extend at least _____ from the hook. Assume b1 = 40 in., b2 = 16 in., d1 = 8 in., d2 = 29 in., and that there are three No. 7 longitudinal tension bars and No. 3 stirrups at 7 in. o.c. The stirrup hooks are 90°.

Adjacent span loading is the common loading pattern for determining maximum negative moments at supports due to dead load.

Compute φVn for the cross section shown. Assume f’c = 3,000 psi, fyt = 40,000 psi, b = 14 in., d = 25 in., and that there are four No. 8 longitudinal tension bars and No. 3 stirrups at 12 in. o.c.

The strength reduction factor is greater for flexure than for shear because flexure-failure loads are more variable than shear-failure loads.

Web reinforcement is normally provided to ensure that the beam reaches the full _______ capacity.

Mi sobrino pequeño va a en los Pirineos cuando visita España.