Project Job Ref.

Section Sheet no./rev.

1
Calc. by Date Chk'd by Date App'd by Date
P 14-Aug-24

STEEL COMPOSITE BEAM DESIGN (AISC 360)

In accordance with AISC 360-16 using the load and resistance factor design method
Tedds calculation version 1.0.16

Design summary
Overall design status; Pass
Overall design utilisation; 0.117
Description Unit Provided Required Utilization Result
Moment, constr (kip_ft) 2013.75 150.83 0.075 PASS
Shear, constr (kips) 797.07 20.11 0.025 PASS
Moment, comp (kip_ft) 2402.01 281.05 0.117 PASS
Shear, comp (kips) 797.07 37.47 0.047 PASS
Deflection, constr (in) 1.5 -1.56 -1.043 PASS
Deflection, comp (in) 1.5 -1.44 -0.961 PASS

10.000
Primary beams

Secondary beam for design

10.000

30.000

Basic dimensions
Beam span; L = 30.000 ft
Beam spacing on one side; b1 = 10.000 ft
Beam spacing on other side; b2 = 10.000 ft
Deck orientation; Deck ribs perpendicular to beam
Profiles are assumed to meet all dimensional criteria in AISC 360-16
Overall depth of slab; t = 5.000 in
Height of ribs; hr = 1.500 in
Centers of ribs; ribccs = 6.000 in
Average width of rib; wr = 2.500 in
Material properties
Concrete
 Project Job Ref.

Section Sheet no./rev.

2
Calc. by Date Chk'd by Date App'd by Date
P 14-Aug-24

Specified compressive strength of concrete; f’c = 3.00 ksi

Wet density of concrete; wcw = 150 lb/ft3
Dry density of concrete; wcd = 130 lb/ft3
Modulus of elasticity of concrete; Ec = wcd1.5 × (f’c × 1 ksi) /(1 lb/ft3)1.5 = 2567 ksi
Steel
Specified minimum yield stress of steel; Fy = 50 ksi
Modulus of elasticity of steel; ES = 29000 ksi
Loading – secondary beam
Weight of slab construction stage; wslab_constr = [t – hr  (1 – wr / ribccs)]  wcw = 51.563 psf
Weight of slab composite stage; wslab_comp = [t – hr  (1 – wr / ribccs)]  wcd = 44.687 psf
Weight of steel deck; wdeck = 3.000 psf
Additional dead load; wd_add = 0.000 psf
Weight of steel beam; wbeam_s = 305.000 lb/ft
Weight of construction live load; wconstr = 20.000 psf
Superimposed dead load; wserv = 10.000 psf
Weight of wall parallel to span; ww_par = 0.000 lb/ft
Weight of wall perpendicular to span; ww_perp = 0.000 lb/ft ;assumed to be at mid-span.
Floor live load; wimp = 80.000 psf
Lightweight partition load; wpart = 10.000 psf
Total construction stage dead load; wconstr_D = [(wslab_constr+wdeck+wd_add)×((b1+b2)/2)] + wbeam_s = 850.625 lb/ft
Total construction stage live load; wconstr_L = wconstr × (b1 + b2) / 2 = 200.000 lb/ft
Total composite stage dead load(excluding walls); wcomp_D = [(wslab_comp+wdeck+wd_add+wserv)(b1+b2)/2]+wbeam_s = 881.875 lb/ft
Total composite stage live load; wcomp_L = (wimp + wpart)  (b1 + b2)/2 = 900.000 lb/ft;

Design forces – secondary beam

Max ultimate moment at construction stage; Mconstr_u = ( 1.2  wconstr_D + 1.6  wconstr_L )  L2/ 8 = 150.834 kips_ft
Max ultimate shear at construction stage; Vconstr_u = ( 1.2  wconstr_D + 1.6  wconstr_L )  L / 2 = 20.111 kips
Maximum ultimate moment at composite stage;
Mcomp_u = ( 1.2  wcomp_D + 1.6  wcomp_L )  L2/ 8 + 1.2 × ww_par × L2/8 + 1.2 × ww_perp × (b1 + b2)/2 × L/4= 281.053 kips_ft
Maximum ultimate shear at composite stage;
Vcomp_u = ( 1.2  wcomp_D + 1.6  wcomp_L )  L / 2 + 1.2  ww_par  L / 2 + 1.2  ww_perp × (b1 + b2)/2 × 1/2= 37.474 kips
Point of max. B.M. from nearest support; LBM_near = L/2 =15.00 ft
Steel section check
Trial steel section; W12X305
Plastic modulus of steel section; Zx = 537.00 in3
Elastic modulus of steel section; Sx = 435.00 in3
Width to thickness ratio; f= bf / ( 2  tf ) = 2.435
Limiting width to thickness ratio (compact); pf = 0.38  (ES / Fy) = 9.152
Limiting width to thickness ratio (noncompact); rf = (ES / Fy) = 24.083
Flange is compact
Depth to thickness ratio (h/tw); w = 5.980
Limiting depth to thickness ratio (compact); pw= 3.76  (ES / Fy) = 90.553
Limiting depth to thickness ratio (noncompact); rw= 5.70 (ES / Fy) = 137.274
Web is compact
 Project Job Ref.

Section Sheet no./rev.

3
Calc. by Date Chk'd by Date App'd by Date
P 14-Aug-24

Strength check at construction stage for flexure

Check for flexure
Plastic moment for steel section; Mp = Fy Zx = 2237.500 kip_ft
Resistance factor for flexure; b = 0.90
Design flexural strength of steel section alone; Mconstr_n = b × Mp = 2013.750 kip_ft
Required flexural strength; Mconstr_u = 150.834 kip_ft
PASS - Beam bending at construction stage loading

Strength check at construction stage for shear

Web area; Aw = d × tw = 26.569 in2
Web plate buckling coefficient; kv = 5.34
Depth to thickness ratio (h/tw); w = 5.980
Web shear coefficient; Cv1 = 1.00
Resistant factor for shear; v = 1.0
Design shear strength; Vconstr_n = v × (0.6  Fy × Aw × Cv1) = 797.070 kips
Required shear strength; Vconstr_u = 20.111 kips
PASS - Beam shear at construction stage loading
Design of steel anchors
Note - for non-uniform stud layouts a higher concentration of studs should be located towards the ends of the beam
Effective slab width of composite section; b = min(L/8, b1/2) + min(L/8,b2/2) = 90.000 in
Effective area of concrete flange; Ac = b  (t – hr) = 315.00 in2
Diameter of stud anchor; dia = 0.750 in
Length of stud anchor after weld; Hs = 3.00 in
Specified tensile strength of stud anchor; Fu = 65 ksi
Cross section area of one stud anchor; Asa =   dia2 / 4 = 0.442 in2
Maximum diameter permitted; diamax = 2.5 × tf = 6.775 in
PASS - Diameter of stud anchor provided is OK
Point of max. B.M. from nearest support; LBM_near = 15.00 ft
No. of ribs from points of zero to max moment; ribnumbers = int(LBM_near /ribccs -1) = 29
No. of ribs with 1 stud per rib; Nr1 = 29
No. of ribs with 2 studs per rib; Nr2 = 0
No. of ribs with 3 studs per rib; Nr3 = 0
Total number of studs; Nprov = Nr1 + 2Nr2 + 3Nr3 = 29
Group effect factor for 1 stud per rib; Rg1 = 1.00
Group effect factor for 2 studs per rib; Rg2 = 0.85
Group effect factor for 3 studs per rib; Rg3 = 0.70
Value of emid-ht is less than 2 in (51 mm)
Position effect factor for deck perpendicular; Rp = 0.60
Nom. strength of one stud with 1 stud per rib; Qn1 = min(0.5 × Asa × (f’c × Ec) , Rg1 × Rp × Asa × Fu ) = 17.230 kips
Nom. strength of one stud with 2 studs per rib; Qn2 = min(0.5 × Asa × (f’c × Ec) , Rg2 × Rp × Asa × Fu ) = 14.645 kips
Nom. strength of one stud with 3 studs per rib; Qn3 = min(0.5 × Asa × (f’c × Ec) , Rg3 × Rp × Asa × Fu ) = 12.061 kips
Total strength of provided steel anchors; Ssc = Nr1Qn1 + 2Nr2Qn2 + 3Nr3Qn3 = 499.66 kips
Resistance of concrete flange; Ccf = 0.85 × f’c × Ac = 803.250 kips
Resistance of steel beam; Tsb = A × Fy = 4475.000 kips
 Project Job Ref.

Section Sheet no./rev.

4
Calc. by Date Chk'd by Date App'd by Date
P 14-Aug-24

Beam/slab interface shear force; C = min(Ccf, Tsb) = 803.250 kips

Strength of studs is less than maximum interface shear force therefore partial composite action takes place
Strength check at partial composite action
Actual net tensile force ; Vh = C = 803.250 kips
Assuming plastic neutral axis at the bottom of the steel beam flange.
Resultant compressive force at flange bottom; Pyf = bf × tf × Fy = 1788.600 kips
Net force at steel and concrete interface; Cnet = Tsb – 2  Pyf = 897.800 kips
PNA is in the web of the I Section
Shear connection force; Fshear = Ssc = 499.66 kips
Total depth of concrete at full stress; dc = Fshear / (0.85 × f’c × b) = 2.177 in
Depth of compression from top of the steel flange; t’ = A / (2 × tw ) – bf  tf / tw - 0.85 f’c/ Fybdc / (2 × tw)+tf = 5.153 in
Tension
Bottom flange component; Fbf = Fy  bf × tf = 1788.600 kips
Moment capacity of bottom flange; Mbf = Fbf  (d – (tf /2) – t’) = 1459.561 kip_ft
Web component; Fweb_t = Fy  (A – (2 bf × tf )-(t’-tf)tw)= 698.730 kips
Moment capacity of web; Mweb_t = Fweb_t  (d –t’ - tf)/2 = 245.645 kip_ft
Compression
Web component; Fweb_c = Fy  (t’-tf)tw= 199.070 kips
Moment capacity of web; Mweb_c= Fweb_c  (t’ - tf)/2 = 20.260 kip_ft
Top flange component; Ftf = Fy  bf × tf = 1788.600 kips
Moment capacity of top flange; Mtf = Ftf  (t’– tf/2) = 566.028 kip_ft
Concrete flange component; Fcf = 0.85 × f’c × b  dc = 499.660 kips
Moment capacity of concrete flange; Mcf = Fcf  (t - dc/2 +t’) = 377.410 kip_ft
Design flexural strength of beam; Mcomp_n = b ( Mbf + Mweb_t + Mweb_c + Mtf + Mcf) = 2402.014 kip_ft
Required flexural strength; Mcomp_u = 281.053 kip_ft
PASS - Beam bending at partial composite stage
Check for shear
Design shear strength; Vcomp_n = Vconstr_n = 797.070 kips
Required shear strength; Vcomp_u = 37.474 kips
PASS - Beam shear at partial composite stage loading
Check for deflection (Commentary section I3.1)
Calculation of immediate construction stage deflection;
Deflection due to dead load; short_D = 5 × wconstr_D × L4 / (384 × ES × Ix) = 0.1506 in
Amount of beam camber; camber = 1.750 in
WARNING - The camber exceeds the construction stage dead load deflection
Deflection due to construction live load; 2 = 5 × wconstr_L × L4 / (384 × ES × Ix) = 0.0354 in
Net total construction stage deflection; short = short_D + 2 - camber = -1.564 in
For short term loading:-
Short term modular ratio; ns = ES / Ec = 11.3
Depth of neutral axis from top of concrete;
ys = [b(t-hr)/ns(t-hr)/2 + A(t+d/2)] / [b(t-hr)/ns+A]
ys = 10.442 in
Moment of inertia of fully composite section;
 Project Job Ref.

Section Sheet no./rev.

5
Calc. by Date Chk'd by Date App'd by Date
P 14-Aug-24

Is = Ix + A(d/2+t-ys)2 + b(t - hr)3/(12ns) + b(t - hr)/ns  (ys - (t-hr)/2)2

Is = 6342 in4
Effective mt of inertia for partially composite; Is_eff = 0.75  [Ix + (Fshear / C)  (Is - Ix)] = ;4313.8; in4
Proportion of live load which is short term; rL_s = 67 %
Deflection due to short term live load; L_s = 5 × rL_s  wcomp_L × L4 / (384 × ES × Is_eff) = 0.0878 in
For long term loading:-
Long term concrete modulus as % of short term; rE_l = 50 %
Long term modular ratio; nl = ES / (Ec  rE_l) = 22.6
Depth of neutral axis from top of concrete;
yl = [b(t-hr)/nl(t-hr)/2 + A(t+d/2)] / [b(t-hr)/nl+A]
yl = 11.613 in
Moment of inertia of fully composite section;
Il = Ix + A(d/2+t-yl)2 + b(t - hr)3/(12nl) + b(t - hr)/nl  (yl - (t-hr)/2)2
Il = 5132 in4
Effective mt of inertia for partially composite; Il_eff = 0.75  [Ix + (Fshear / C)  (Il - Ix)] = ;3598.3; in4
Proportion of live load which is long term; rL_l = 1 - rL_s = 33 %
Deflection due to long term live load; L_l = 5 × rL_l  wcomp_L × L4 / (384 × ES × Il_eff) = 0.0519 in
Dead load due to parallel wall & superimp. dead; wD_part = ww_par + (wserv(b1+ b2) / 2) = 100.0000 lb/ft
Long term deflection due to superimposed dead load (after concrete has cured):-
Wall parallel to span and superimposed dead; 4 =5 × (wD_part) × L4 / (384 × ES × Il_eff) = 0.0175 in
Wall perpendicular to span; 5 =(ww_perp (b1+ b2) / 2) × L3 / (48 × ES × Il_eff) = 0.0000 in

Combined deflections
Net total construction stage deflection; short = short_D + 2 - camber = -1.564 in
Net total long term deflection; long = short_D + L_s + L_l + 4 + 5 - camber = -1.442 in
Combined short and long term live load deflectn; live = L_s + L_l = 0.140 in
Net long term dead and super imposed dead defln; dead = short_D +4 + 5 - camber = -1.582 in
Post composite deflection; comp = L_s + L_l + 4 + 5 = 0.157 in
Allowable max deflection; Allow = 1.500 in
PASS - Deflection less than allowable
Arrangement of steel anchor
Note - for non-uniform stud layouts a higher concentration of studs should be located towards the ends of the beam;

Location of maximum bending moment

15.000 15.000
29 ribs with 1 stud per rib Studs as other half of beam