Calculating Moment of a Beam | PSU Professional Portfolio

[rodsika]

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

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??

 

[AlephZero]

20 feet = 6.096 meters, not 6.

 

[rodsika]

20 feet = 6.096 meters, not 6.

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.. :)

 

[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?

 

[pmacias]

I would like to clarify the discrepancy between the two calculations for the moment of a beam. The first calculation, using the formula Mu= w L^2 / 8, is the correct way to calculate the moment of a beam. However, there seems to be a mistake in the conversion between units in the second calculation.

The conversion between lb-ft and kN-m is not a direct conversion, as they are measuring different quantities (force and torque). Therefore, simply multiplying by a conversion factor will not give an accurate result.

In the first calculation, the units of lb-ft are used to represent the moment of the beam, which is a measure of torque. In the second calculation, the units of kN-m are used, which represent a force multiplied by a distance. This is not the same as the moment of a beam.

To accurately convert between lb-ft and kN-m, you would need to use the formula 1 lb-ft = 1.3558 N-m. This takes into account the difference between force and torque. Using this conversion, the result of 48424 ft-lb would be equal to 65832.78 N-m, which is closer to the 50,000 lb-ft calculated in the first method.

In conclusion, it is important to be careful when converting between units, especially when dealing with different quantities such as force and torque. Using the correct conversion factors and formulas will ensure accurate results in scientific calculations.