About Composite Beam Calculator
The composite beam calculator analyses a steel section acting compositely with a concrete slab. It computes the effective slab width, the modular ratio used to transform the concrete to equivalent steel, the elastic neutral axis and transformed moment of inertia, and the plastic moment capacity Mp for ductile full-composite design.
It follows the transformed-section method for elastic stiffness and a rectangular concrete stress block for plastic strength. The tool automatically selects whether the plastic neutral axis lies in the slab (the concrete can resist all of the steel tension) or in the steel section, and reports the governing effective-width term and the depth of the concrete stress block.
How It Works
- Enter the steel section properties: area As, depth d, yield strength Fy, and second moment of area Is.
- Enter the slab thickness ts, concrete strength fc', and the steel flange width bf used in the effective-width check.
- Enter the beam span L and spacing s for the effective slab width, plus the elastic moduli Es and Ec for the modular ratio.
- The calculator finds be = min(L/4, s, 16ts + bf), transforms the slab by n = Es/Ec, locates the elastic neutral axis, and computes the plastic moment Mp from the steel yield force and the concrete compression block.
Worked Example
A composite beam has a steel section with As = 6000 mm^2, d = 400 mm, Fy = 355 MPa, supporting a slab ts = 120 mm with fc' = 30 MPa. With span L = 8000 mm, spacing s = 2500 mm and flange bf = 200 mm, the effective width is be = min(8000/4, 2500, 16*120 + 200) = min(2000, 2500, 2120) = 2000 mm (span/4 governs). Using Es = 200000 and Ec = 25000 the modular ratio is n = 8 and the transformed width is be/n = 250 mm. The steel tension force is T = As*Fy = 6000*355 = 2,130,000 N = 2130 kN, while the full slab can carry Cc = 0.85*30*2000*120 = 6,120,000 N = 6120 kN. Since Cc >= T the plastic neutral axis lies in the slab. The stress block depth is a = (As*Fy)/(0.85*fc'*be) = 2,130,000/51,000 = 41.76 mm, giving Mp = As*Fy*(d/2 + ts - a/2) = 2,130,000*(200 + 120 - 20.88) = 637.1 kN.m.
Formulas
- Effective slab width
be = min( L/4, s, 16*ts + bf )- Modular ratio and transformed width
n = Es / Ec, b_tr = be / n- Elastic neutral axis (transformed section)
(b_tr/2)*y^2 + As*y - As*(ts + d/2) = 0- Plastic moment -- PNA in slab (CASE A, Cc >= T)
a = (As*Fy)/(0.85*fc'*be), Mp = As*Fy*( d/2 + ts - a/2 )- Plastic moment -- PNA in steel (CASE B, Cc < T)
Cc = 0.85*fc'*be*ts, Cs = (T - Cc)/2, Mp = Cc*(ts/2 + d/2) + Cs*(d/2)
Standards & References
- AISC 360 (Specification for Structural Steel Buildings) — Chapter I, Composite Members
- Eurocode 4 EN 1994-1-1 (Design of composite steel and concrete structures)
- Plastic and transformed-section analysis
Frequently Asked Questions
How is the effective slab width determined?
The effective width is the smallest of three limits: a quarter of the span L/4, the beam spacing s, and 16 times the slab thickness plus the flange width (16ts + bf). The calculator reports which of the three terms governs.
What is the modular ratio and why transform the section?
The modular ratio n = Es/Ec scales the stiffer steel relative to the softer concrete. To analyse the section elastically as one material, the concrete slab is replaced by an equivalent steel area using a reduced width be/n, giving the transformed section.
When does the plastic neutral axis fall in the slab versus the steel?
If the full slab compression Cc = 0.85*fc'*be*ts is at least the steel yield force T = As*Fy, the concrete alone resists all the steel tension and the PNA sits in the slab (CASE A). If the slab is too weak (Cc < T), the PNA drops into the steel (CASE B) and part of the steel acts in compression.
What assumptions are built into the plastic capacity?
It assumes full composite action with a ductile, fully-yielded steel section and a rectangular (Whitney) concrete stress block at 0.85*fc'. Shear-connector capacity, partial composite action, and construction-stage stresses are not included and must be checked separately.