The general theory of composite beam design calculations is well known among structural engineers, however, the execution of composite beam design in practice necessitates taking into account a number of factors in addition to structural calculations, such as fire engineering, constructability, and more. This article discusses the structural design of composite beams and some of the factors that must be taken into account while designing composite beams.

The construction industry in the United States of America now uses two basic approaches to composite beam design – The LRFD and ASD methods. The method featured in the 3rd Edition LRFD Manual of Steel Construction is both simpler in design and more cost-effective than the method described in the 9th Edition Manual of Steel Construction (ASD).

In the ASD method, the moment capacity is computed from the superposition of elastic stresses, while in the LRFD approach, the moment capacity is computed from the distribution of plastic stresses.

It is usually possible to produce an economical design with partial composite action in the beam. In many design situations, increasing the beam size can satisfy the design moment while significantly reducing the number of studs needed. The design of composite beams is almost always carried out using computer software or design tools like those found in the AISC Manual.

The deck size should, within reason, be chosen to allow for the beam spacing. For un-shored construction, the Steel Deck Institute (SDI) offers tables that show the maximum span permitted for a specific deck and slab arrangement. In general, the economy of the steel floor system is improved by maximizing the span for a given deck size, for un-shored construction. It is advised that you choose a deck assuming a 2-span un-shored condition and avoid single-span situations as much as possible.

The ponding of concrete as well as how the slab is poured must be taken into account. You might want to factor in an extra 1/2 inch of concrete to accommodate for ponding when estimating the amount of concrete needed to construct level slabs. Since the wet weight of lightweight concrete has been reported in the field to range up to 125 pcf, it is crucial to consider this.

**Materials for Composite Beam Construction**

All of the approved ASTM material specifications for the construction of composite floors are included in Section A3 of the AISC Specification. During the design of composite beams, it is pertinent to always specify ASTM A992 when broad flange beams are being used. However, HSS, pipes, and built-up shapes are also covered by the AISC requirements. The ASTM A108 shear stud, which has a tensile strength of 60 ksi, is frequently used in specifications. 3/4-inch diameter studs are the most typical size used in building construction.

In addition to reinforcing bars and welded wire, the composite slab may also be steel fibre reinforced in accordance with ASTM C1116 in specific circumstances. For normal-weight concrete and light-weight concrete, the minimum specified compressive strength of the concrete in the slab must be between 3 ksi and 10 ksi. Higher strengths should only be relied upon for rigidity. In order to comply with standard fire-rated assemblies, 3.5 ksi normal-weight concrete and 3 ksi light-weight concrete are typically specified.

**Cambering in Composite Beams**

Although there are several ways to obtain level steel-framed floors, cambering of beams is the technique of choice in the United States. Engineers in the field frequently misunderstand the purposes of proper beam cambering. Beam camber is just one component of a comprehensive floor levelness strategy that must take into account the slab pour method, building occupancy, and steel fabrication and installation procedure.

The main objective of cambering beams is to accurately predict how much the beam will actually deflect under the weight of the concrete. Correct camber is best attained between 75 and 80 percent of the estimated dead load deflection because of connection restraints and fabrication tolerances. Beams should never have excessive camber. Additionally, cambering is improper for a variety of beam types, including brace beams and very short beams.

**Serviceability of Composite Beams**

For composite floors, serviceability factors to be taken into account are long-term deflections from the superimposed dead load, short-term deflections from the live load, vibration control, and slab system performance. The acceptance standards relevant to the intended floor use, creep deflections under superimposed dead load, and partial composite action must all be taken into account when evaluating deflections.

**Design and Detailing of Studs**

The 1999 AISC Specification’s Section 15.6 addresses proper stud design and detailing. In the longitudinal and transverse directions, the minimum stud spacing is 6 times and 4 times the stud diameter, respectively. Two new factors—stud geometry and stud position inside the deck ribs—will need to be taken into account in accordance with the 2005 Specification.

**Design Example of Composite Beams**

Design a 25ft long secondary beam in a proposed commercial complex. The deck ribs are perpendicular to the beam, and the secondary beams are spaced at 10 ft intervals. The concrete for the steel deck has an overall depth of 6 inches with a compressive strength of 3 ksi. The following loadings are anticipated on the floor;

Weight of steel deck = 3.000 psf

Additional dead load= 20.000 psf

Weight of steel beam = 54.000 lb/ft

Weight of construction live load = 20.000 psf

Floor live load = 40.000 psf

Lightweight partition load = 10.000 psf

**Basic dimensions**

Beam span; L = 25.000 ft

Beam spacing on one side; b_{1} = 10.000 ft

Beam spacing on the other side; b_{2} = 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 = 6.000 in

Height of ribs; h_{r} = 1.500 in

Centers of ribs; rib_{ccs} = 6.000 in

Average width of rib; w_{r} = 2.500 in

Material properties

**Concrete**

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

Wet density of concrete; w_{cw }= 150 lb/ft^{3}

Dry density of concrete; w_{cd }= 130 lb/ft^{3}

Modulus of elasticity of concrete; E_{c} = w_{cd}^{1.5} × √(f’_{c} × 1 ksi) /(1 lb/ft^{3})^{1.5} = 2567 ksi

**Steel**

Specified minimum yield stress of steel; F_{y} = 50 ksi

Modulus of elasticity of steel; E_{S} = 29000 ksi

**Loading – secondary beam**

Weight of slab construction stage; w_{slab_constr} = [t – h_{r} × (1 – w_{r} / rib_{ccs})] × w_{cw} = 64.062 psf

Weight of slab composite stage; w_{slab_comp} = [t – h_{r} × (1 – w_{r} / rib_{ccs})] × w_{cd} = 55.521 psf

Weight of steel deck; w_{deck} = 3.000 psf

Additional dead load; w_{d_add} = 20.000 psf

Weight of steel beam; w_{beam_s} = 54.000 lb/ft

Weight of construction live load; w_{constr} = 20.000 psf

Floor live load; w_{imp} = 40.000 psf

Lightweight partition load; w_{part} = 10.000 psf

Total construction stage dead load;

w_{constr_D} = [(w_{slab_constr} + w_{deck} + w_{d_add}) × ((b_{1}+b_{2})/2)] + w_{beam_s} = 924.625 lb/ft

Total construction stage live load;

w_{constr_L} = w_{constr} × (b_{1} + b_{2}) / 2 = 200.000 lb/ft

Total composite stage dead load(excluding walls);

w_{comp_D} = [(w_{slab_comp} + w_{deck} + w_{d_add} + w_{serv}) × (b_{1} + b_{2})/2] + w_{beam_s} = 839.208 lb/ft

Total composite stage live load;

w_{comp_L} = (w_{imp} + w_{part}) × (b_{1} + b_{2})/2 = 500.000 lb/ft;

**Design forces – secondary beam**

Max ultimate moment at construction stage;

M_{constr_u} = ( 1.2w_{constr_D} + 1.6w_{constr_L }) × L^{2}/ 8 = 111.684 kips_ft

Max ultimate shear at the construction stage;

V_{constr_u} = ( 1.2w_{constr_D} + 1.6w_{constr_L} ) × L/2 = 17.869 kips

Maximum ultimate moment at the composite stage;

M_{comp_u} = ( 1.2w_{comp_D} + 1.6w_{comp_L }) × L^{2}/ 8 + 1.2 × w_{w_par} × L^{2}/8 + 1.2w_{w_perp} × (b_{1} + b_{2})/2 × L/4 = 141.176 kips_ft

Maximum ultimate shear at the composite stage;

V_{comp_u} = ( 1.2w_{comp_D} + 1.6w_{comp_L} ) × L/2 + 1.2 × w_{w_par} × L/2 + 1.2w_{w_perp} × (b_{1} + b_{2})/2 × 1/2= 22.588 kips

Point of max. B.M. from nearest support;

L_{BM_near} = L/2 = 12.50 ft

**Steel section check**

Trial steel section; W10X54

Plastic modulus of steel section; Z_{x} = 66.60 in^{3}

Elastic modulus of steel section; S_{x} = 60.00 in^{3}

Width to thickness ratio; λ_{f} = b_{f} / ( 2t_{f} ) = 8.130

Limiting width to thickness ratio (compact); λ_{pf} = 0.38 × √(E_{S} / F_{y}) = 9.152

Limiting width to thickness ratio (non-compact); λ_{rf} = √(E_{S} / F_{y}) = 24.083

Flange is compact

λ_{w} = h_to_t_{w} = 21.200

Depth to thickness ratio (h/t_{w});_{ }λ_{w} = 21.200

Limiting depth to thickness ratio (compact); λ_{pw}= 3.76 × √(E_{S} / F_{y}) = 90.553

Limiting depth to thickness ratio (noncompact); λ_{rw}= 5.70 × √(E_{S} / F_{y}) = 137.274

Web is compact

Strength check at the construction stage for flexure

**Check for flexure**

Plastic moment for steel section; M_{p} = F_{y}Z_{x} = 277.500 kip_ft

Resistance factor for flexure; φ_{b} = 0.90

Design flexural strength of steel section alone;

M_{constr_n} = f_{b} × M_{p} = 249.750 kip_ft

Required flexural strength; M_{constr_u} = 111.684 kip_ft

PASS – Beam bending at construction stage loading

**Strength check at the construction stage for shear**

Web area; A_{w} = d × t_{w} = 3.737 in^{2}

Web plate buckling coefficient; k_{v} = 5.34

Depth to thickness ratio (h/t_{w});_{ }λ_{w} = 21.200

Web shear coefficient; C_{v1} = 1.00

Resistant factor for shear; φ_{v} = 1.0

Design shear strength; V_{constr_n} = φ_{v} × (0.6F_{y} × A_{w} × C_{v1}) = 112.110 kips

Required shear strength; V_{constr_u} = 17.869 kips

PASS – Beam shear at construction stage loading

**Design of shear connectors**

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, b_{1}/2) + min(L/8, b_{2}/2) = 75.000 in

Effective area of concrete flange; A_{c} = b(t – h_{r}) = 337.50 in^{2}

Diameter of shear stud; dia = 0.750 in

Length of shear stud after weld; H_{s} = 3.00 in

Specified tensile strength of shear stud; F_{u} = 65 ksi

Cross section area of one shear stud; A_{sc} = π × dia^{2} / 4 = 0.442 in^{2}

Maximum diameter permitted; dia_{max} = 2.5 × t_{f} = 1.537 in

PASS – Diameter of shear stud provided is OK

Point of max. B.M. from nearest support;

L_{BM_near} = 12.50 ft

No. of ribs from points of zero to max moment;

rib_{numbers} = int(L_{BM_near} /rib_{ccs} -1) = 24

No. of ribs with 1 stud per rib; N_{r1} = 24

No. of ribs with 2 studs per rib; N_{r2} = 0

No. of ribs with 3 studs per rib; N_{r3} = 0

Total number of studs; N_{prov} = N_{r1} + 2N_{r2} + 3N_{r3} = 24

Group effect factor for 1 stud per rib; R_{g1} = 1.00

Group effect factor for 2 studs per rib; R_{g2} = 0.85

Group effect factor for 3 studs per rib; R_{g3} = 0.70

Value of e_{mid-ht} is less than 2 in (51 mm)

Position effect factor for deck perpendicular; R_{p} = 0.60

Nom. strength of one stud with 1 stud per rib;

Q_{n1} = min(0.5 × A_{sc} × √(f’_{c} × E_{c}) , R_{g1} × R_{p} × A_{sc} × F_{u} ) = 17.230 kips

Nom. strength of one stud with 2 studs per rib;

Q_{n2} = min(0.5 × A_{sc} × √(f’_{c} × E_{c}) , R_{g2} × R_{p} × A_{sc} × F_{u} ) = 14.645 kips

Nom. strength of one stud with 3 studs per rib;

Q_{n3} = min(0.5 × A_{sc} × √(f’_{c} × E_{c}) , R_{g3} × R_{p} × A_{sc} × F_{u} ) = 12.061 kips

Total strength of provided shear connectors;

S_{sc} = N_{r1}Q_{n1} + 2N_{r2}Q_{n2} + 3N_{r3}Q_{n3} = 413.51 kips

Resistance of concrete flange; C_{cf} = 0.85f’_{c}A_{c} = 860.625 kips

Resistance of steel beam; T_{sb} = AF_{y} = 790.000 kips

Beam/slab interface shear force; C = min(C_{cf}, T_{sb}) = 790.000 kips

The strength of studs is less than the maximum interface shear force therefore partial composite action takes place

Strength check at partial composite action

Actual net tensile force; V_{h} = C = 790.000 kips

Assuming a plastic neutral axis (PNA) at the bottom of the steel beam flange.

Resultant compressive force at flange bottom;

P_{yf} = b_{f} × t_{f} × F_{y} = 307.500 kips

Net force at steel and concrete interface;

C_{net} = T_{sb} – 2P_{yf} = 175.000 kips

PNA is in the flange of I Section

Shear connection force;

F_{shear} = S_{sc} = 413.51 kips

Total depth of concrete at full stress;

d_{c} = F_{shear} / (0.85 × f’_{c} × b) = 2.162 in

Depth of compression from top of the steel flange;

t’ = A / (2 × b_{f} ) – 0.85f’_{c} / F_{y}bd_{c} / (2 × b_{f} ) = 0.376 in

**Tension**

Bottom flange component;

F_{bf} = F_{y}b_{f} × t_{f} = 307.500 kips

Moment capacity of bottom flange;

M_{bf} = F_{bf}(d – (t_{f} /2) – t’) = 241.285 kip_ft

Web component;

F_{web} = F_{y}(A – (2b_{f} × t_{f} ))= 175.000 kips

Moment capacity of web;

M_{web} = F_{web}[((d – 2t_{f})/2)+ t_{f} – t’] = 68.155 kip_ft

Top flange component;

F_{tf_t} = F_{y}b_{f} × (t_{f} – t’) = 119.256 kips

Moment capacity of top flange;

M_{tf_t} = F_{tf_t} (t_{f} – t’)/2 = 1.185 kip_ft

**Compression**

Top flange component;

F_{tf_c} = F_{y}b_{f} × t’ = 188.244 kips

Moment capacity of top flange;

M_{tf_c} = F_{tf_c}t’/2 = 2.953 kip_ft

Concrete flange component;

F_{cf} = 0.85f’_{c} × bd_{c} = 413.512 kips

Moment capacity of concrete flange;

M_{cf} = F_{cf}(t – d_{c}/2 + t’) = 182.476 kip_ft

Design flexural strength of beam;

M_{comp_n} = f_{b}( M_{bf} + M_{web} + M_{tf_t} + M_{tf_c} + M_{cf}) = 446.450 kip_ft

Required flexural strength;

M_{comp_u} = 141.176 kip_ft

PASS – Beam bending at partial composite stage

**Check for shear**

Design shear strength;

V_{comp_n} = V_{constr_n} = 112.110 kips

Required shear strength;

V_{comp_u} = 22.588 kips

PASS – Beam shear at partial composite stage loading

**Check for deflection (Commentary section 13.1)**

Calculation of immediate construction stage deflection;

Deflection due to dead load;

D_{short_D} = 5 × w_{constr_D} × L^{4} / (384 × E_{S} × I_{x}) = 0.9248 in

Amount of beam camber; D_{camber} = 0.000 in

PASS – The camber is less than the construction stage dead load deflection

Deflection due to construction live load;

D_{2} = 5 × w_{constr_L} × L^{4} / (384 × E_{S} × I_{x}) = 0.2000 in

Net total construction stage deflection;

D_{short} = D_{short_D} + D_{2} – D_{camber} = 1.125 in

For short-term loading:-

Short-term modular ratio;

n_{s} = E_{S} / E_{c} = 11.3

Depth of neutral axis from the top of concrete;

y_{s} = [b(t – h_{r})/n_{s}(t – h_{r})/2 + A(t + d/2)] / [b(t – h_{r})/n_{s} + A]

y_{s} = 5.294 in

Moment of inertia of fully composite section;

I_{s} = I_{x} + A(d/2 + t – y_{s})^{2} + b(t – h_{r})^{3}/(12n_{s}) + b(t – h_{r})/n_{s}(y_{s} – (t – h_{r})/2)^{2}

I_{s} = 1154 in^{4}

F_{shear} = S_{sc} = 413.5 kips

Effective of inertia for partially composite;

I_{s_eff} = 0.75[I_{x} + √(F_{shear} / C) × (I_{s} – I_{x})] = 688.9 in^{4}

Proportion of live load which is short term; r_{L_s} = 67 %

Deflection due to short-term live load;

D_{L_s} = 5r_{L_s}w_{comp_L}L^{4} / (384E_{S}I_{s_eff}) = 0.1474 in

For long-term loading:

Long term concrete modulus as % of short term; r_{E_l} = 50 %

Long-term modular ratio;

n_{l} = E_{S} / (E_{c}r_{E_l}) = 22.6

Depth of neutral axis from top of concrete;

y_{l} = [b(t – h_{r})/n_{l} × (t – h_{r})/2 + A(t + d/2)] / [b(t – h_{r})/n_{l} + A]

y_{l} = 6.773 in

Moment of inertia of fully composite section;

I_{l} = I_{x} + A(d/2 + t – y_{l})^{2} + b(t – h_{r})^{3}/(12n_{l}) + b(t – h_{r})/n_{l} (y_{l} – (t – h_{r})/2)^{2}

I_{l} = 923 in^{4}

Effective moment of inertia for partially composite;

I_{l_eff} = 0.75[I_{x} + √(F_{shear} / C)(I_{l} – I_{x})] = 563.6 in^{4}

Proportion of live load which is long term;

r_{L_l} = 1 – r_{L_s} = 33 %

Deflection due to long-term live load;

D_{L_l} = 5 × r_{L_l} ´ w_{comp_L} × L^{4} / (384 × E_{S} × I_{l_eff}) = 0.0887 in

Dead load due to parallel wall & superimp. dead;

w_{D_part} = w_{w_par} + (w_{serv}(b_{1}+ b_{2}) / 2) = 0.0000 lb/ft

**Long-term deflection due to superimposed dead load (after concrete has cured)**

Wall parallel to span and superimposed dead;

D_{4} =5 × (w_{D_part}) × L^{4} / (384 × E_{S} × I_{l_eff}) = 0.0000 in

Wall perpendicular to span;

D_{5} =(w_{w_perp}(b_{1}+ b_{2}) / 2) × L^{3} / (48 × E_{S} × I_{l_eff}) = 0.0000 in

**Combined deflections**

Net total construction stage deflection;

D_{short} = D_{short_D} + D_{2} – D_{camber} = 1.125 in

Net total long-term deflection;

D_{long} = D_{short_D} + D_{L_s} + D_{L_l} + D_{4} + D_{5} – D_{camber} = 1.161 in

Combined short and long-term live load deflection;

D_{live} = D_{L_s} + D_{L_l} = 0.236 in

Net long-term dead and superimposed dead deflection;

D_{dead} = D_{short_D} +D_{4} + D_{5} – D_{camber} = 0.925 in

Post composite deflection;

D_{comp} = D_{L_s} + D_{L_l} + D_{4} + D_{5} = 0.236 in

Allowable max deflection;

D_{Allow} = 1.250 in

PASS – Deflection less than allowable