ARCH 523bl - Fall 2024
Homework 4
Problem 1
A reinforced concrete beam has a rectangular cross-section as shown in Figure 1.
a) Calculate the steel reinforcement area.
b) Calculate the steel reinforcement ratio.
Given:
• Compressive strength, f’c= 4,000 psi
• Rebar yield strength, fy= 60 ksi
• Rebars: 4 No. 9
Parameters:
• b= 12 in
• d= 17 in
• clear cover, cc= 2 in
Figure 1- Beam Cross Section
Problem 2
For the beam cross-section in Problem 1, determine:
a) The minimum steel reinforcement area required by the ACI 318 code.
b) The minimum steel reinforcement ratio required by the ACI 318 code.
c) Does the provided reinforcement meet the code requirements?
Problem3
For the beam cross-section in Problem 1, determine:
a) Whether the section is tension-controlled, or compression controlled.
b) Strength reduction factor for bending.
Problem 4
A single-span reinforced concrete beam is uniformly loaded as shown in Figure 2. The beam cross section is provided in Problem 1. Verify if the beam bending strength is adequate for the applied loads.
Given:
• Distributed superimposed dead load, qSDL= 400 lbf/ft
• Distributed live load, PLL= 8 kip
• Weight of concrete, sw= 150 lbs/ft3 (normal weight)
Parameters:
• L= 40 ft (span)
Figure 2- Simply Supported Beam
Hint:
1. Calculate the self-weight of the beam (lbs/ft) and add to super superimposed dead load to obtain the DL distributed load.
2. Use Tabulated Moments and Deflections for Beams provided in the lecture notes 3.
Problem 5
A concrete hanger and a concrete beam are shown in Figure 3.
Which one of these members must be designed with tension reinforcement? Please explain your answer.
Figure 3- Concrete Members
Problem 6
A retaining concrete wall is supported at the top and base and is resisting soil pressure as shown in Figure 4.
a) Does the wall need tension reinforcement? Please explain your answer.
b) If reinforcement is required, show where the replacement needs to be placed, close to side A or B? (provide a sketch)
Figure 4- Concrete Wall