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# Re: Beam design

• To: <seaint(--nospam--at)seaint.org>
• Subject: Re: Beam design
• From: "rizmirza" <rizmirza(--nospam--at)lhr.comsats.net.pk>
• Date: Mon, 9 Jan 2006 22:07:57 +0500

```Santosh:

This is how I feel about it.

```
```From basic equilibrium:
```
```
Case-1: Moment (Mu) + Axial Tension (Nu)
```
First assume that the axial force is tensile. Shift your axial force to the center of steel reabars. Now you have moved the tensile force, Nu, by (d - h/2) and have introduced a moment equal to Nu * (d-h/2), acting in the same direction as the external moment. To correct for the additional moment, subtract this moment from your actual design moment and you have a statically equivalent system. In this equivalent system, Nu is acting at the center of rebars and the applied moment has been reduced by Nu * (d-h/2). Design for the reduced moment and add additional reinforcement required for Nu.
```
Mus = Mu - Nu (d-h/2)
As1 = Reinforcement required for Mus
As2 = Nu / (Phi x fy)
As = As1 + As2
Provide As in the beam.

Case-2: Moment (Mu) + Axial Compression (Nu)
```
Now assume that the axial force is compressive. Again, shift your axial force to the center of steel reabars. Like before, you have moved the compressive force, Nu, by (d - h/2) and have introduced a moment equal to Nu * (d-h/2), but acting in the direction opposite to the external moment. To correct for the additional moment, add this moment to your actual design moment and you have a statically equivalent system. In this equivalent system, Nu is acting at the center of rebars and, this time, the applied moment has been increased by Nu * (d-h/2). Design for the increased moment and subtract additional reinforcement required for Nu.
```
Mus = Mu + Nu (d-h/2)
As1 = Reinforcement required for Mus
As2 = Nu / (Phi x fy)
As = As1 - As2
Provide As in the beam.

where
h = Total depth of the beam section.
d = Effective depth of the beam section.
fy = Yield stress of rebars
Phi = Capacity reduction factor of ACI 318.

```
Keep your units consistent. If you are working in the customary American units and if the moment is in Kip-feet, Nu should be in Kips and (d-h/2) should be in feet, so that you get Mus in Kip-feet. When computing As2, if the yield stress in KSI and Nu is in Kip, you would get your rebar area directly in square inches.
```
```
As to considering the beam with axial force as a column, it is correct that the basic equilibrium and compatibility equations would apply all the same. But the capacity reduction factor of ACI 318 would be different for a beam. Except for this, it is the same.
```
```
And, Santosh, I do not think that a young person with an engineering degree should be able to do it right away; one has to learn it. So do not take to heart the discouraging comment of a colleague. <Smile>
```
I hope it helps.

Rizwan Mirza
Rizwan Mirza, Consulting Engineers
Lahore, Pakistan

```
----- Original Message ----- From: "Santhosh Kumar Yedidi" <sant527(--nospam--at)gmail.com>
```To: <seaint(--nospam--at)seaint.org>
Sent: Monday, January 09, 2006 2:41 PM
Subject: Beam design

```
```How to do beam design with axial forces acting.

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