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Composite Beam to AISC 360's banner

Composite Beam to AISC 360

Verified by the CalcTree engineering team on October 17, 2024

This calculator computes the flexural and shear capacity of a composite beam, which consists of W-shaped steel members and a concrete slab. It computes the number of shear studs required to achieve fully composite action.
All calculations are performed in accordance with the AISC 360-22 (16th Edition).


Results Summary

Summary 
Design Check
Action
Resistance
Utilisation
Status
Flexural Strength
Mu = 325.0 kips
ΦbMn = 972.9632352941179 foot * kip
M_utilisation: .2f
🟢
Shear Strength
Vu = 225.0 kips
ΦvVn = 225.22500000000002 inch ** 2 * kip_per_square_inch
V_utilisation: .2f
🟢
Can’t display the image because of an internal error. Our team is looking at the issue.



Calculation

Technical notes

  1. The design follows LRFD (Load and Resistance Factor Design) principles, using factored loads and corresponding resistance factors as per AISC 360-16.
  2. The composite beam consists of a W-shaped steel section and a reinforced concrete (RC) slab.
  1. The boundary condition for the beam is assumed to be pinned on both ends.
  1. The entire horizontal shear at the interface between the steel beam and concrete slab is assumed to be transferred by steel-headed studs.
  1. The number of studs is fixed to ensure a fully composite beam according to the conditions from the user inputted stud strength, diameter and number of studs per row. Fully composite action is achieved by calculating how many studs is required for
    
    .
  2. Reinforcement in the slab is not included for ULS design since the RC slab is assumed not to contribute any tensile resistance. Only the steel beam is assumed to provide tensile resistance to the flexural strength of the composite beam. However, reinforcement is provided to the slab in practice for crack control, but this check is out of the scope of this calculator.
  1. All current ASTM A6/A6M W-shapes have compact webs for
    
    ≤ 70 ksi (485 MPa), this means that the width-to-thickness ratio of the web
    
    is not larger than
    
    (AISC 360 I3.2a).
  1. The design case assumes no transverse web stiffeners and specifies the web panel location as an interior web panel, aligned with the structural design requirements.

1. Properties

1.1 Concrete Slab



wc
:145lb/ft3​



t
:4.00 in​



f'c
:4.00 ksi​




Ec
:3,492.06 ksi​




Ch. I8.2da


1.2 Steel Beam



L
:20.00 ft​



s
:10.00 ft​



Fy,b
:50 ksi​



Fu
:65 ksi​

Beam span (center-to-center of supports)





16.80 in²​
16.40 in​
14.97 in​
14.19 in​
7.1 in​
0.43 in​
0.715 in​

Symbols

  1. 
    
    is the cross-sectional area of the member
  2. 
    
    is the overall depth of the member
  3. 
    
    is the distance of the web between the flanges (Including radius corners)
  1. 
    
    is the clear distance of the web between the flanges
  2. 
    
    is the flange width
  3. 
    
    is the web thickness
  4. 
    
    is the flange thickness


1.3 Steel Anchors



Fy,s
:50.00 ksi​



Fu,s
:65.00 ksi​



nr
:2​



dsa
:0.625in​



n_sr
:28.00​



s_sr
:8.57 in​



nst
:56.00​

= Number of rows from to





2. Design Actions



M
:325.0 kips ft​



V
:200.0 kips​



3. Design Checks

3.1 Flexural Check

3.1.1 Steel anchors

Stud anchor capacity calculation determines the shear strength of each headed stud anchor in a composite beam. These anchors transfer shear forces between the steel beam and concrete slab, ensuring they act together fully or partially as a single structural element.
Steel anchors required on each side of the point of maximum bending moment

shall be distributed uniformly between that point and the adjacent points of zero moment (AISC360−Ch.I8.2d(a)).
The nominal shear strength of one steel-headed stud

is calculated by:

Qn=min⁡{0.5Asafc′EcRgRpAsaFu,sQ_n= \min\begin{cases} 0.5A_{sa}\sqrt{f'_cE_c}\\R_gR_pA_{sa}F_{u,s}\end{cases}
Where:
  1. 
    
    is the cross-sectional area of a steel-headed stud anchor.
  2. 
    
    and
    
    are the system configuration factors where
    
    for any number of steel-headed stud anchors welded in a row directly to the steel shape, as in this case where there aren't steel decks (I8.2aRg(b)).
    
    In this case where the steel-headed stud anchors are welded directly to the steel shape (I8.2aRp(a)).
The shear strength between the section of maximum bending moment, and the adjacent section of zero moment

, is calculated by the capacity of one steel-headed stud multiplied by the number of steel-headed studs between the section of maximum bending moment, and the adjacent section of zero moment

.

∑Qn=Qnnst\sum Q_n = Q_n n_{st}
Full composite action is achieved by ensuring

, which is done in this calculator.


Qn
:14.96 kips​




Eqn. I8-1


ΣQn
:837.55 kip​




Eqn. C-I3-8


3.1.2 Effective width of the concrete slab

According to AISC 360 Ch. I3.1a, the effective width of the concrete slab

is determined as the sum of the effective widths on either side of the beam’s centerline, with each side not exceeding the specified maximum width given by:
  1. One-eighth of the beam span, center-to-center of supports.
  2. One-half the distance to the centerline of the adjacent beam.

b=min⁡{2×L82×s2b=\min\begin{cases}2 \times \frac {L}{8} \\ 2 \times \frac {s}{2}\end{cases}
Where:
  1. 
    
    is the beam span (center-to-center of supports).
  2. 
    
    is the average distance between beams (centerline-to-centerline).
Effective width of the concrete slab



b
:5.00 ft​




Cl. I3.1a

3.1.3 Plastic neutral axis

The plastic neutral axis (P.N.A.) is where the stresses transition from compression (in the concrete slab) to tension (in the steel beam).
The location of the P.N.A. depends on the relative strength of the steel and concrete. The more effective the concrete slab is in compression, the higher the P.N.A. will be within the steel beam. If the P.N.A. is located higher in the steel beam, more of the steel is engaged in tension, and less of the concrete is required for compression.
There are 3 possible locations for the P.N.A.:
(a) Within the concrete slab.
(b) Within the flange of the steel beam.
(c) Within the web of the steel beam.
P.N.A. possible locations.

Fully composite behavior refers to the condition in a composite beam where the steel member and concrete slab act as a single unit to their full capacity. This is achieved when the shear connectors (such as studs) are sufficient to transfer all the shear forces between the steel and concrete, allowing the materials to work together without relative slip.
As these calculations are for a beam in fully composite action, the compression force

in the concrete slab is governed by the smallest of the:
  1. yield strength of the steel section:
    
    
  1. compressive strength of the concrete:
    
    
Where

is the area of the concrete slab within effective width and

is the cross-sectional area in tension of the member.
This means that the shear connectors are sufficient to transfer all the shear forces between the steel and concrete, allowing the materials to act together as a single unit.
Plastic stress distribution for positive moment in composite beams.


Explore the toggles below for more information about how to determine the location of the P.N.A.

Case a): P.N.A. located in the concrete slab

In the case where the compression force is equal to the yield strength of the steel section (

), the P.N.A. is located in the concrete slab, and its depth

can be calculated using the following equation:

a=C0.85fc′ba = \frac {C} {0.85f'_c b}
The distance from the centroid of the compression force in the concrete slab to the top of the steel section

is equal to:

.


Case b) & c): P.N.A. located in the steel beam

When the P.N.A. is located in the steel beam, it is necessary to determine whether it is located in the flange or in the web. We can achieve this by comparing the compressive capacity of the flange with the compressive force in the steel beam:
  1. If
    
    , the P.N.A is in the flange, as per case b)
  2. If
    
    , the P.N.A is in the web, as per case c)
Where according to AISC 360 Ch. C.I3.2a:
  1. 
    
    is the compressive capacity of the flange
  2. 
    
    is the compressive force in the steel beam
And by the equilibrium between compression and tension,

.
If P.N.A is in the flange as per case b), we can calculate the depth of the P.N.A. from the top of the flange

with the following equation:

d(b)={0 ;  (a)CsbfFy,b ; (b)d3−d(c) ; (c)d_{(b)} = \begin{cases} 0 \ ; \ \ (a) \\ \frac{C_s}{b_f F_{y,b}} \ ; \ (b) \\ d_3 - d_{(c)} \ ; \ (c) \end{cases}
And the distance from the centroid of the compression force in the steel section to the top of the steel section

is:

d2=d(b)/2d_2 = d_{(b)}/2
If P.N.A is in the flange as per case b), we can locate the P.N.A. at a distance

from the bottom of the top flange using this equation:

d(c)=Cs−CftwFy,bd_{(c)} = \dfrac {C_s - C_f}{t_w F_{y,b}}
And the distance from

to the top of the steel section

can be calculated as:

d3=d−ycd_3 = d - y_c
Where

is the centroid of the remaining steel in tension.

Calculation of





Case
:(b)​


P.N.A Location
:P.N.A is located at the depth of 0.03 in from the top of the steel beam​



Cc
:780.00 kip​




Eqn. C-I3-6


Ct
:780.00 kip​



Eqn. C-I3-8


Cf
:254.54 kip​




Cl. I3.2a


Cs
:12.00 kip​



Cl. I3.2a


d1
:2.00 in​




Cl. I3.2a


d2
:0.02 in​



Cl. I3.2a


d3
:8.41 in​




Cl. I3.2a


yc
:7.99 in​





3.1.4 Flexural capacity

According to the AISC 360 I3.2a, the design positive flexural strength,

and allowable positive flexural strength

, shall be determined for the limit state of yielding as follows.
Where:



The nominal plastic moment strength of a composite beam in positive bending is given by:

Mn=C(d1+d2)+Py(d3−d2)M_n=C(d_1+d_2)+P_y(d_3-d_2)
Case (a)

Case (b)

Case (c)



C
:816.00 kip​




Cl. I3.2a


Py
:828.00 kip​




Cl. I3.2a


Mn
:716.2 ft kip​




Eqn. C-I3-10


ΦMn
:644.5 ft kip​



Utilisation_M
: 0.5 🟢​





3.2 Shear Check

3.2.1 Web shear coefficient

The web shear strength coefficient

is determined by:

Cv1={1.10kvE/Fy,bh/tw; if h/tW>1.10E/Fy,b1.0; elseC_{v1} = \begin{cases} \frac {1.10 \sqrt{k_v E/F_{y,b}}}{h/t_w} ; \text{ if}\ h/t_W > 1.10\sqrt{E/F_{y,b}}\\ 1.0 ; \text{ else} \end{cases}


Cv1
:1.00​





Ch. G2.2.1(1)(ii)

3.2.2 Shear capacity

According to the AISC 360 I3.4.3, the design shear strength,

, and allowable shear strength,

, of composite beams with steel-headed studs shall be determined based upon the properties of the steel section alone in accordance with Chapter G.

Vn=0.6Fy,bAwCv1V_n = 0.6F_{y,b}A_wC_{v1}
The web plate shear buckling coefficient,

for webs without transverse stiffeners is

as per AISC 360 Ch. G2.2.1(2)(i).
The resistance factor for shear

is determined by:

ϕv={1.0;  if  h/tW≤2.24E/Fy,b0.9; else\phi_v = \begin{cases} 1.0; \ \text{ if} \ \ h/t_W ≤ 2.24\sqrt{E/F_{y,b}}\\ 0.9 ; \ \text{else} \end{cases}


Vn
:211.6 kip​




Eq: G2-1


ΦVn
:211.6 kip​



Utilisation_V
: 0.95 🟢​






Related Resources

  1. Composite Slab to ACI 318
  2. Steel Beam and Column Designer to AISC 360
  3. Concrete Rectangular Beam Calculator to ACI 318-19 (IMP)