Composite Floor Beams

Composite Floor Beams

Floor beams and slab were designed as a fully composite system to reduce beam sizes and to take advantage of the concrete floor strength. Floor beams were designed with the following properties:

Total floor depth - 6.25 inches

Concrete fill - Lightweight concrete (fc’= 3ksi, 110pcf density)

Steel strength - fy = 50ksi

Shear studs - ¾ inch diameter 3 inches long

Shored and unshored construction was evaluated with the following assumed construction loads

Wet concrete - 60 psf live load

Additional const. load – 20 psf live load

Finally, the choice of using composite beams was verified by performing a cost comparison between composite and non-composite beams.

A. Loads
Loads were obtained from load key sheets. Three typical loadings and three floor beam lengths/spacings were used in calculations.

Dead Load - 85psf

Live Load - Heavy =(150psf), Medium = (100psf) and Light = (50psf)

Floor beams - 30'Long @10' spacing, 25'@10' and 25' @8'-4"

B. Required Flexural Strength

The flexural resistance required was obtained from:

Formula Mu = 1/8 w L^2

where w is the load per linear foot of beam obtained from tributary widths (half the distance to adjacent beams) and L is the span of the beam.

C. Select Section and Properties

Assuming the depth is the concrete stress block, a, is less than the thickness of the concrete slab, the design flexural strength, φMn is:

Formula φMn = φAsFy(d/2 + y_conc – a/2)

where As is the area of the steel beam required, d is the depth of the steel beam (assumed to be 10” for the first iteration), yconc is 6.25 inches, a is the depth of the concrete block (assumed to be 2” for the first iteration).

A value of Y2 , distance from top of the steel flange to the center of the concrete stress block, is also required. Assuming the depth of the concrete stress block is less then the thickness of the slab, Y2 was obtained from:

Formula Y2 = y_conc – a/2

Using these two values sections were chosen from the AISC LRFD Steel Design Manual 3rd edition Table 5-14 Composite W-Shapes.

Flexural capacity was check using:

Formula φMn = φAsfy (d/2 + y_conc + a/2)

Where b = 2* min(1/8 beam span or 0.5 distance to centerline of the adjacent beam)

And where a is given by:

a =<fyAs>/<0.85fc’b

D. Compute number of Shear Studs Required

The nominal strength of 1 stud was obtained from:

Qn = 0.5 Asc sqrt(fc’ Ec)<= AscFu

where Asc is the cross-section of the shear stud (0.44in2) , Ec is the the modulus of elasticity of concrete given below (2085.3 ksi) and w is the unit weight of concrete (110pcf).

Ec = 33*(w1.5) sqrt(fc’)

For a ¾ in diameter stud the strength is 17.47 kips.

The number of studs required from the point of max moment to its connected ends for full composite action was obtained from:

# = (As fy)/Qn

Since the beams are simply supported this number is for half the beam length.

Total number of studs required is then twice #.

E. Construction Phase Strength Check

A flexural demand for an unshored beam was check using the construction loads assumed. For floor beams where the flexural capacity of the steel is exceeded, a larger section was chosen and the number of shear studs recalculated.

F. Deflection Calculations

Beams that are unshored were checked for deflection under dead loads using:

/delta = <5wL^4>/<384 E I

where unfactored load per linear foot of beam and E and I are the modulus of elasticity and moment of inertia for the unshored beam. Where deflection are large (δ>L/360) adequate cambering is required.

Beams that are composite were checked for deflections under live loads using:

/delta = <5wL^4>/<384 E I <= L/360

where w is the unfactored load per linear foot on the beam, E is the modulus of elasticity for the steel beam and I is the lower bond elastic moment of inertia given Table 5-15 of the AISC LRFD Steel Design Manual 3rd edition.

G. Comparison to a Non-Composite Section

Beam sections were chosen by comparing flexural capacity of the steel section to the calculated flexural strength required. Sections chosen were also checked for live load deflections as (δ<L/360).

Assuming 7lbs per stud (in cost) the amount of steel increase due to the beam size increase was compared.

Sizes for each of the 3 loadings (heavy, medium and light) and for each of the 3 spans/spacings as described in A, are tabulated below. A sample calculation can be found in the Appendix.

Section Design

Heavy (LL = 150psf) / 30'@10'
Type of Const / Section / Stud / Stud Spacing / Mu [kft] / φMn [kft]
Shored / W12x35 / 3/4" / every 6" / 384.75 / 439.5
Unshored / W12x35 / 3/4" / every 6" / 144 / 192
Non-Composite / W16x57 / 384.75 / 394
Heavy / 25'@10'
Type of Const / Section / Stud / Stud Spacing / Mu [kft] / φMn [kft]
Shored / W14x22 / 3/4" / every 8" / 267.2 / 280
Unshored / W14x22 / 3/4" / every 8" / 100 / 124.5
Non-Composite / W16x40 / 267.2 / 274
Heavy / 25'@8.333'
Type of Const / Section / Stud / Stud Spacing / Mu [kft] / φMn [kft]
Shored / W10x22 / 3/4" / every 8" / 222.57 / 255
Unshored / W10x22 / 3/4" / every 8" / 83.3 / 97.5
Non-Composite / W16x36 / 222.57 / 240
Medium(LL = 100psf) / 30'@10'
Type of Const / Section / Stud / Stud Spacing / Mu [kft] / φMn [kft]
Shored / W10x26 / 3/4" / every 8" / 294.75 / 302.1
Unshored / W12x30 / 3/4" / every 7" / 144 / 161.6
Non-Composite / W16x45 / 294.75 / 308.6
Medium / 25'@10'
Type of Const / Section / Stud / Stud Spacing / Mu [kft] / φMn [kft]
Shored / W10x19 / 3/4" / every 9" / 204.7 / 224
Unshored / W10x26 / 3/4" / every 6" / 100 / 117.4
Non-Composite / W14x34 / 204.7 / 204.75
Medium / 25'@8.333'
Type of Const / Section / Stud / Stud Spacing / Mu [kft] / φMn [kft]
Shored / W10x15 / 3/4" / every 11" / 170.5 / 176.4
Unshored / W10x22 / 3/4" / every 8" / 83.3 / 97.5
Non-Composite / W14x34 / 170.5 / 204.75
Light (LL = 50psf) / 30'@10'
Type of Const / Section / Stud / Stud Spacing / Mu [kft] / φMn [kft]
Shored / W10x19 / 3/4" / every 11" / 204.75 / 226.72
Unshored / W12x30 / 3/4" / every 7" / 144 / 161.6
Non-Composite / W14x34 / 204.75 / 204.75
Light / 25'@10'
Type of Const / Section / Stud / Stud Spacing / Mu [kft] / φMn [kft]
Shored / W10x12 / 3/4" / every 14" / 142.2 / 142.34
Unshored / W10x26 / 3/4" / every 6" / 100 / 117.4
Non-Composite / W14x26 / 142.2 / 139.5
Light / 25'@8.333'
Type of Const / Section / Stud / Stud Spacing / Mu [kft] / φMn [kft]
Shored / W10x12 / 3/4" / every 14" / 118.4 / 142.34
Unshored / W10x22 / 3/4" / every 8" / 83.3 / 97.5
Non-Composite / W12x26 / 118.4 / 139.5

Cost Comparison

Heavy / 30'@10'
Type of Const / Section / length / spacing (in) / Num stud / weight ea / extra weight / use
Shored / W12x35 / 30 / 6 / 60 / 7 / 420 / W12x35
Unshored / W12x35 / 30 / 6 / 60 / 7 / 420
Non-Composite / W16x57 / length / non comp wt / comp wt / diff / weight diff / use
30 / 57 / 35 / 22 / 660
Heavy / 25'@10'
Type of Const / Section / length / spacing (in) / Num stud / weight ea / extra weight / use
Shored / W14x22 / 25 / 8 / 38 / 7 / 266 / W14x22
Unshored / W14x22 / 25 / 8 / 38 / 7 / 266
Non-Composite / W16x40 / length / non comp wt / comp wt / diff / weight diff / use
25 / 40 / 22 / 18 / 450
Heavy / 25'@8.333'
Type of Const / Section / length / spacing (in) / Num stud / weight ea / extra weight / use
Shored / W10x22 / 25 / 8 / 38 / 7 / 266 / W10x22
Unshored / W10x22 / 25 / 8 / 38 / 7 / 266
Non-Composite / W16x36 / length / non comp wt / comp wt / diff / weight diff / use
25 / 36 / 22 / 14 / 350
Medium / 30'@10'
Type of Const / Section / length / spacing (in) / Num stud / weight ea / extra weight / use
Shored / W10x26 / 30 / 8 / 45 / 7 / 315 / W10x26
Unshored / W12x30 / 30 / 7 / 52 / 7 / 364
Non-Composite / W16x45 / length / non comp wt / comp wt / diff / weight diff / use
30 / 45 / 30 / 15 / 450
Medium / 25'@10'
Type of Const / Section / length / spacing (in) / Num stud / weight ea / extra weight / use
Shored / W10x19 / 25 / 9 / 34 / 7 / 238 / W10x19
Unshored / W10x26 / 25 / 6 / 50 / 7 / 350
Non-Composite / W14x34 / length / non comp wt / comp wt / diff / weight diff / use
25 / 34 / 19 / 15 / 375
Medium / 25'@8.333'
Type of Const / Section / length / spacing (in) / Num stud / weight ea / extra weight / use
Shored / W10x15 / 25 / 11 / 28 / 7 / 196 / W10x15
Unshored / W10x22 / 25 / 8 / 38 / 7 / 266
Non-Composite / W14x34 / length / non comp wt / comp wt / diff / weight diff / use
25 / 34 / 22 / 12 / 300
Light / 30'@10'
Type of Const / Section / length / spacing (in) / Num stud / weight ea / extra weight / use
Shored / W10x19 / 30 / 11 / 33 / 7 / 231 / W10x19
Unshored / W12x30 / 30 / 7 / 52 / 7 / 364
Non-Composite / W14x34 / length / non comp wt / comp wt / diff / weight diff / use
30 / 34 / 19 / 15 / 450
Light / 25'@10'
Type of Const / Section / length / spacing (in) / Num stud / weight ea / extra weight / use
Shored / W10x12 / 25 / 14 / 22 / 7 / 154 / W10x12
Unshored / W10x26 / 25 / 6 / 50 / 7 / 350
Non-Composite / W14x26 / length / non comp wt / comp wt / diff / weight diff / use
25 / 26 / 12 / 14 / 350
Light / 25'@8.333'
Type of Const / Section / length / spacing (in) / Num stud / weight ea / extra weight / use
Shored / W10x12 / 25 / 6 / 50 / 7 / 350 / W10x12
Unshored / W10x22 / 30 / 6 / 60 / 7 / 420
Non-Composite / W12x26 / length / non comp wt / comp wt / diff / weight diff / use
Roof / 30'@10'
Type of Const / Section / length / spacing (in) / Num stud / weight ea / extra weight / use
Shored / W10x12 / 30 / 17 / 22 / 7 / 154 / W10x12
Unshored / W12x30 / 30 / 7 / 52 / 7 / 364
Non-Composite / W10x26 / length / non comp wt / comp wt / diff / weight diff / use
30 / 26 / 12 / 14 / 420
Roof / 25'@10'
Type of Const / Section / length / spacing (in) / Num stud / weight ea / extra weight / use
Shored / W10x12 / 25 / 14 / 22 / 7 / 154 / W10x12
Unshored / W10x26 / 25 / 6 / 50 / 7 / 350
Non-Composite / W10x19 / length / non comp wt / comp wt / diff / weight diff / use
25 / 19 / 12 / 7 / 175
2nd Floor Mech / 30'@10'
Type of Const / Section / length / spacing (in) / Num stud / weight ea / extra weight / use
Shored / W12x58 / 30 / 3 / 120 / 7 / 840 / W12x58
Unshored / W12x58 / 30 / 3 / 120 / 7 / 840
Non-Composite / W16x89 / length / non comp wt / comp wt / diff / weight diff / use
30 / 89 / 58 / 31 / 930

APPENDIX

Sample Calculation of Floor beams and cost comparison

Design of Floor System
Composite Floor Beam info
conc. Strength, fc' / 3 / ksi
Beam Length, L / 30 / ft
Floor beam spacing, s / 10 / ft
Yield Strength, Fy / 50 / ksi
Ultimate strength, Fu / 70 / ksi
Conc thickness, yconc / 6.25 / in
Conc Lightweight or Normal / Lightweight / <choose
If lightweight, unit weight conc,w / 110 / pcf
Service Load
Dead Load, DL / 85 / psf
Live Load, LL / 100 / psf / 0.085 / ksf
0.1 / ksf
Load Factors
DL factor / 1.2
LL factor / 1.6
Resistance Factor
φ / 0.9
A. Factored load along floor beam
DL / 1.02 / k/ft
LL / 1.6 / k/ft
TOTAL / 2.62 / k/ft
B. Required Flexural Strength /
Moment Demand, Mu / 294.75 / kft
Moment Demand, Mu / 3537 / kin
C. Select Section and Determine Properties
assume:
steel depth, d / 10 / in
depth of conc block, a / 2 / in
Composite table parameters
Area of steel, As / 7.67 / in^2
top of steel to conc centrd,Y2 / 5.25 / in
Assumed Section / W10x26 / <-Base your choice on composite beam selection table from AISC LRFD Steel Manual
Section Area / 7.61 / in^2
Depth, d / 10.33 / in^2
factored bending capacity,φMp / 117.375 / kft
Moment of inertia, Ixx / 144 / in^4
Concrete Slab
effective width, b = min of(
floor beam spacing / 10 / ft
two sides of 1/8 span) / 7.5 / ft
effective width, b = / 7.5 / ft
Check assumptions
depth of conc stress block, a / 1.66 / in
factored bending capacity,φMn / 3625.18 / kin
factored bending capacity,φMn / 302.10 / kft / OR From composite tables
OK use section
Composite Property
Ixx / 490 / in^4 / From Composite talbes Lower bound elastic moment of inertia
D. Compute Number of Shear Studs Required
Shear stud Diameter / 3/4 / in
shear stud area / 0.44 / in^2 / <choose
Ec / 2085.28 / ksi
Shear stud strength / 17.47 / kips
or / 30.93 / kips
Shear stud strength / 17.47 / kips
Required number of shear studs for full composite
Number / 21.8 / each
for half the span or / 15 / ft
Place 1 stud every / 8 / inches
SHORED
Section / W10x26
With Shear stud sized / 3/4 / in
Spaced 1 every / 8 / inches
E. Unshored Construction Check
wet concrete unit weight,LL / 60.00 / psf
Misc. construciton load,LL / 20.00 / psf
Factored Load / 1.28 / k/ft
Moment demand, Mu / 144.00 / kft
Capcity / 117.38 / kft
Section Fails REDESIGN
Redesign if necessary
Assumed Section / W12x30 / <-Base your choice on composite beam selection table from AISC LRFD Steel Manual