Analyze the reinforced concrete beam below. Note the steel is a 60ksi yield. fc= 4000 psi fy=60

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Question:

Analyze the reinforced concrete beam below.

Note the steel is a 60ksi yield. f’c= 4000 psi fy=60 ksi Es= 29,000 ksi As= 4.00in2

b = 12 fc = 4000 psi fy =60 ksi d = 22 h = 24 As=4.00 in.2 Strain Stress

1)Find the depth of the Whitney stress block and the neutral axis: a = _____________(in) c =______________(in).

2)Tensile and compressive forces. T = ______________C = ______________.

3)Find thearm and nominal moment capacity. arm = _________(in) Mn= ______________kip-ft.

4)Sketch the strain and stress diagrams(above) and identify all important points.

5)Use the strain diagram to find the strain in the steel when concrete crushes. εt=________________.

6)Is the section usable according to ACI? _______Why or why not?___________ Which section of ACI applies to this?__________________.

7)Compute the design strength. Mn=___________________kip-ft.

8)If the amount of steel is increased from 4.0 in^2to 6.0 in^2 or a 50% increment of steel reinforcements for this beam, the design strength Mn will increase ____ %.

9)If the depth of the beam is increased by 2 in., i.e., h = 26 in. and d = 24 in., the design strength Mn will increase ____ %.

10)If the width of the beam is increased from b = 12 in. to b = 14 in., the design strength Mn will increase ____ %.1

1)From 8) to 10), we can change the size of the beam or increase the number of reinforcements to increase the design strength Mn of the beam. But in practice, we also need to avoid excessive deflection of the beam. Which approach is the best to meet both strength and stiffness requirements? ________________.