JDstruc
Active member
I'm working on Problem 603 of the NCEES Structural SE practice exam. It is a 1-way slab problem, regarding moments and shears in the beam.
My question is regarding how they are calculating "Ln" for various conditions, shown on page 100. The center-to-center span is 30'-0", and the columns are all 24" square. I would assume that Ln is the clear distance, which would be 30' - 24"/2 - 24"/2 = 28'-0". Yet the solution is using a different value for Ln...in fact, they are using multiple values. From the solution:
End span, Ln = 30.0 - 2.0 - 2.0/2 = 27 feet
Interior span, Ln = 30.0 - 2.0/2 - 2.0/2 = 28 feet
Ln = (27 + 28) /2 (average...???)
They use Ln=27.0 for the Positive Moment M+ = wLn^2/14
They use Ln=27.5 for Negative Moment M- = wLn^2/10 or wLn^2/16 (at 1st interior support, and at exterior column respectively)
Then they use Ln=27.0 for the shear reactions, V = 1.15wLn/2 or wLn/2 (at end member, and at all others)
So...
1) Why is Ln not simply 28.0 for all conditions?
2) Why are they using different Ln values, for calculating various items for THE SAME BEAM?
I'm rather confused. Any clarification would be greatly appreciated. Thanks all.
My question is regarding how they are calculating "Ln" for various conditions, shown on page 100. The center-to-center span is 30'-0", and the columns are all 24" square. I would assume that Ln is the clear distance, which would be 30' - 24"/2 - 24"/2 = 28'-0". Yet the solution is using a different value for Ln...in fact, they are using multiple values. From the solution:
End span, Ln = 30.0 - 2.0 - 2.0/2 = 27 feet
Interior span, Ln = 30.0 - 2.0/2 - 2.0/2 = 28 feet
Ln = (27 + 28) /2 (average...???)
They use Ln=27.0 for the Positive Moment M+ = wLn^2/14
They use Ln=27.5 for Negative Moment M- = wLn^2/10 or wLn^2/16 (at 1st interior support, and at exterior column respectively)
Then they use Ln=27.0 for the shear reactions, V = 1.15wLn/2 or wLn/2 (at end member, and at all others)
So...
1) Why is Ln not simply 28.0 for all conditions?
2) Why are they using different Ln values, for calculating various items for THE SAME BEAM?
I'm rather confused. Any clarification would be greatly appreciated. Thanks all.