A rectangular beam with cross section b = 16 in., h = 20 in., and d = 17.5 in. supports a total factored uniform load of 2.00 kips/ft, including its own dead load. The beam is simply supported with a 21-ft span. It is reinforced with four No. 7 Grade 60 bars, two of which are cutoff between midspan and the support and two of which extend 10 in. past the centers of the supports. The concrete strength is 3,000 psi (normal weight). The beam has Grade 60 No. 3 stirrups satisfying ACI 318-14 Sections 9.7.6.2.2 and 9.6.3.3. The strength of the four bars is φMn = 169.9 kip-ft, and the strength of the remaining two bars is φMn = 89.74 kip-ft. Determine the distance from the support to the theoretical cutoff point (i.e. disregard ACI 318-14 Section 9.7.3.3).

A simply supported beam with dimensions of b = 14 in., h = 30 in., d = 27.5 in., and L = 24 ft supports a uniform service (unfactored) dead load of 1.5375 kips/ft including its own self weight plus a uniform service (unfactored) live load of 1.2 kips/ft. The beam is reinforced with two No. 5 Grade 60 bars. The concrete strength is 7,600 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Using the effective moment of inertia, determine the immediate mid-span deflection of the beam due to the combined service loads (dead plus live).The effective moment of inertia Ie = 8,000 in.4.

A rectangular beam has a cross section of b = 16 in., h = 28 in., and d = 25.5 in. It is reinforced with two No. 5 Grade 60 bars. The concrete strength is 4,600 psi (normal weight). The beam has Grade 60 No. 3 stirrups satisfying ACI 318-14 Sections 9.7.6.2.2 and 9.6.3.3. Determine the strength φMn for this beam.

Which is generally shorter?

A rectangular beam has a cross section of b = 18 in., h = 28 in., and d = 25.5 in. It is reinforced with two No. 7 Grade 60 bars. The concrete strength is 9,400 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the gross moment of inertia, Ig, for the beam.

A beam is singly reinforced with the reinforcement in two rows. The bottom row contains 9 No. 6 bars at a depth of 14 in. The top row contains 7 No. 5 bars at a depth of 8 in. Determine the effective (centroidal) depth, d, of the steel.

Bond stresses lead to splitting _______.

Heads can be attached to one or both ends of a bar by internal threads on the head mating to the bar, welding or forging onto the bar, or by a separate nut used to secure the head onto the bar.

A rectangular beam has a cross section of b = 18 in., h = 30 in., and d = 27.5 in. It is reinforced with two No. 5 Grade 60 bars. The concrete strength is 9,700 psi (normal weight). The beam has Grade 60 No. 3 stirrups. Determine the cracked moment of inertia, Icr. The neutral axis location of the cracked beam (measured from the top of the beam) is 2.9554 in.

The straight line theory is a plastic calculation that gives a good estimate of the concrete and steel stresses at ultimate loads. It is used to calculate the stiffness, EI, at ultimate loads, for deflection calculations, and steel stresses, for use in crack-width or fatigue calculations.