what size i beam for suspended concrete slab

by Lou

Question:

what size i beam for suspended concrete slab?

Answer:
The size of i beam to support suspended slab depends on the length or span of the beam and the load it carries.

Suppose you have a 20 ft x 20 ft garage or storage structure that you want suspended slab over. Assuming the clear span of the beam is 19 feet, clear span means the dimension or length of the beam between the supports at each end. Whether it is walls or columns, see detail 24 below.



Let's figure out what size of wide flange you need. First we need to determine the load that the beam will be subjected to.

Dead load:
metal deck = 2.0 psf
8 inch concrete slab = 150pcf *8/12 = 100 psf
ceiling = 2 psf
beam weight = 30 plf = 30*19/19*10 = 3 psf

Since we don't know what size of beam to use, we assume the beam weigh 30 pounds per foot. The 30x19 give us the total weight of the beam, the 19x10 is the tributary area the beam will be carrying the load. The beam is to be located at the middle of the 20 ft x 20 ft structure. The beam being at the middle will carry half of the load to it's left and right so half of 10ft is 5 ft to both left and right will give us 10ft thus 10x19.

Total Dead load = 107 psf

Live Load = 40 psf (typical garage load)

Total load = 147 psf = 147x10 = 1,470 plf or 1.47 klf

The beam beam formula:
M=wL^2/8 = 1.47x19^2/8=66.3 kip-ft = 796 kip-in

The section modulus formula:
S=M/Fy, where Fy = .66*50ksi(yield strength of steel or i beam)

S = 796/33 = 24 cubic inches

The next step is go to the beam sections properties
Click here to see PDF steel i beam sizes

From the i beam section properties select an Sx value that is 24 cubic inches or more. The possible options are W8x28 S=24.3; W10x26 S=27.9; W12x22 S=25.4; W14x22 S=29 all can do the job.

Since beams are sold by weight, W12x22 and W14x22 will cost about the same because they both weigh 22 lbs/ft. Due to the fact that W14x22 is stronger due to its higher S value, I would use the W14.