Reinforced  Rectangular Concrete Beam Figure
Problem (Example)

Calculator
Notes


Determine the amount of reinforcement 'As" steel required by a rectangular Beam whose cross section is shown in the figure. The factored moment Mu applied at the section point is is 300 kip-in.

Given Data: (see Calculator)

Mu= 300 kip-in

d =14 in

b= 8 in

h= 18 in


fc= 5000 psi

fy= 60,0000 psi

Φ= 0.9   strength reduction factor  

Tension controlled

Try (3) # 4 , As= 0,2*3 = 0.6 in2

Solution:

Reinforced concrete Rectangular cross section subject to flexure loads under the provisions and design  assumption of ACI 318-05  10.2:
ACI 318 10.4 for minimum reiforcemet
ACI 318-05 7.12.2.1 for Minimum for shrinkage & temperature
ACI 318-05 9.3.1 tension controlled design and Φ=0.90

 Analysis Procedure:

Determine reinforcemet ratios  ρ, Min and Max

1- Calculate ρ required for loaded section

2- Calculate ρ Minimums and selecte the greate ρ Min

3- Determine the As Min for shrinkage and Temperatue

4- Calculate the ρ max for tension controlled design 

Evaluate 'As' provided: 

5- Evaluate RoRquired against ρ Minimums

6 - Evaluate 'As'  provided  against minimum and maximum
1 Rn=
=0.2125
1 ρ Req= =0.0036364
2 ρmin= for6     =0.0035354
3 As Min Shrink. & temp
=0.0018 * 8*18
  		 =0.2592 in2
4 Calculate β
ACI 318-05  10.2.7.3 


  		 =0.80
4 ρ max for Tension controlled  design

  =0.021267
5 Evaluate ρ Required
Against minimums 'ρ'
ACI 318-05  10.5.3
4/3*0.0036364=0.004849
0.004849 > 0.0035354
ρ req= 		= 0.0036364
6 ρ Provided
  =0.005357
6 As min Required :
0.0036364*8 *14= 0.407 ,
0.0018 * 8*18= 0.2592 		 =0.407 in2
6  As max for tension controlled  design
0.021267 * 8 * 14=  = 2.3818 in2
  As  Provided Check:  
  		  As= 0.60 in2   Okay!