The figure shown represents the profile and cross section of a reinforced concre
ID: 1710957 • Letter: T
Question
The figure shown represents the profile and cross section of a reinforced concrete beam. Reinforcing is Grade 60 steel, and the 29-day compressive strength of the concrete is 3000 psi. The beam is... (A) Over-reinforced (B) Under-reinforced (C) Balanced (D) Doubly reinforced What is the design moment strength? (A) 20 kip-ft (B) 33 kip-ft (C) 41 kip-ft (D) 53 kip-ft What is the required moment strength? (A) 15 kip-ft (B) 20 kip-ft (C) 24 kip-ft (D) 33 kip-ft Shear reinforcement is... (A) not needed at the mid-span of the beam (B) not needed at the ends of the beam (C) not needed anywhere on the beam (D) needed for the full length of the beamExplanation / Answer
From the given question, one end is hinged and the other end is supported on roller supports hence the moment on the one end will be zero.
Beam Length = 12ft
UDL = 1kip/ft
Beam Dimensions = 15 inches * 6 inches
It is given the beam is singly reinforce with logitudinal reinforcement of 2 * 6 no bars
Considering only longitudinal moment and not transverse moement,
We get,
Given the concrete block is in compresssion, we get,
Xu = 0.87*fy*Ast/(0.361*fck*b)
where fck = grade of concrete = 3000psi
fy = grade of steel = 60psi
Ast = 2 * 0.785* .75*0.75
we get Xu = 1.84 & xu/d = 1.13
xumax/d = 0.87*fy*ptlim/0.361*fck*100
where ptlim = 1.681
we get xumax/d = 1.21
since xumax/d>xu/d the protion is under-reinforced.
A.)UnderReinforced
B.)41kips/ft using equation Mulim = 0.361fck*b*xumax*(d-0.416Xumax)
C.)Required Moment Strength using the same formula is = 24kips
D.) Shear Reinforcement is needed in mid-span of the beam