# Mu of a Beam

1. Sep 25, 2012

### rodsika

http://www.personal.psu.edu/kar5230/blogs/kyles_professional_portfolio/How%20to%20Design%20a%20Singly%20Reinforced%20Concrete%20Beam.pdf [Broken]

I'm stuck with a formula above. It says that to calculate for Moment of a beam... use the formula

Mu= w L^2 / 8

now given w = 1000 lb/ft, L=20 feet... then Mu= w L^2/8 = 1000(20)^2/8 = 50,000 lb-ft
(although it's written as 500,000 lb-ft in the site.. i think it's wrong?)

Anyway. my question is.. i have spent half a day doing conversion from lb-ft to Kilonewton-meter and I can't seem to get it right.

I found out the following formula for converting between the two units:

1 kN - m = 737.56 ft-lb
1 kN/m = 68.52 lb/ft

Now in the above example given w = 1000 lb/ft, L=20 feet

1000 lb/ft = (14.59 kn/m x 6^2) / 2 = 525 kn-m/8 = 65.65 Kn-m

Now converting Kn-m to ft-lb...

65.65 KN-m x 737.56 ft-lbs / 1 KN-m = 48424 ft-lb or (lb-ft I assume this is the same).

Now why can't it be equal to the 50,000 lb-ft in earlier calculation??

Last edited by a moderator: May 6, 2017
2. Sep 25, 2012

### AlephZero

20 feet = 6.096 meters, not 6.

3. Sep 25, 2012

### rodsika

Thanks. I have spent a day trying to find out even going to this particular Theorem in math which says some equations just can't be solved. So 0.1 is significant.. :)

4. Sep 28, 2012

### rodsika

I'm trying to determine the deflection of the above beam. An engineer told me that deflections of beams from 6 meter to 7 meter is non-linear and high that is why many in constructions limit beam span to 6 meters for economy. What do you think of this. Anyway. Let's prove it by formula/calculations. On the following page is online calculator to solve for deflection.

http://civilengineer.webinfolist.com/str/sdcalcuf.php

Supposed span of beam is 6 meters, w of beam is 4.23 Kn/m, distance of deflection measured is at middle, Modulus of Elasticity is 57000x sqrt (fc=21) or 261206, what is the formula or how do you determine the Moment of Inertia so I can input it to the online calculator above, thanks?