# SECTION MODULUS CALCULATOR

Section modulus calculator for I beam, hollow rectangle, rectangle, C channel, T section, circular hollow section, round bar and unequal angle.

Section modulus is the moment of inertia of the area of the cross section of a structural member divided by the distance from the neutral axis to the farthest point of the section; a measure of the flexural strength of the beam. Beam Cross Section I Beam Hollow Rectangle Rectangle C Channel T Section Circular Hollow Section Round Bar Angle Unit System (Quick selection) MetricInch INPUT PARAMETERS Parameter Value Flange-flange inner face height [H] mm cm m inch ft Width [B] Flange thickness [h] Web thickness [b]
 RESULTS Parameter Value Section modulus [Sxx] --- mm^3 cm^3 inch^3 ft^3 Section modulus [Syy] ---

Note: Use dot "." as decimal separator.

### Definitions:

Second Moment of Area: The capacity of a cross-section to resist bending.

### Section Modulus Formula:

 I Beam Section Modulus Formula Parameter Equation Area moment of inertia Ixx = H3b/12 + 2[h3B/12 + hB(H+h)2/4] Area moment of inertia Iyy = b3H/12 + 2(B3h/12) Section modulus Sxx = 2Ixx/(H + 2h) Section modulus Syy = 2Iyy/B
 Hollow Rectangle Section Modulus Formula Parameter Equation Area moment of inertia Ixx = BH3/12 - bh3/12 Area moment of inertia Iyy = HB3/12 - hb3/12 Section modulus Sxx = Ixx/yc Section modulus Syy = Iyy/xc Centroid distance xc=B/2 Centroid distance yc=H/2
 Rectangle Section Modulus Formula Parameter Equation Area moment of inertia Ixx = BH3/12 Area moment of inertia Iyy = HB3/12 Section modulus Sxx = Ixx/yc Section modulus Syy = Iyy/xc Centroid distance xc=B/2 Centroid distance yc=H/2
 C Channel Section Modulus Formula Parameter Equation Area moment of inertia Ixx = H3b/12 + 2[h3B/12 + hB(h+H)2/4] Area moment of inertia Iyy = b3H/12 + bH(xc-b/2)2+ 2B3h/12+ 2Bh(xc - B/2)2 Section modulus Sxx = Ixx/yc Minimum section modulus Syy = Iyy/(B-xc) Centroid distance xc = (2hB2/2 + b2H/2)/A Centroid distance yc= H/2 + h
 T Section Modulus Formula Symbol Equation Area moment of inertia Ixx = bH(yc-H/2)2 + bH3/12 + hB(H + h/2 - yc)2 + h3B/12 Area moment of inertia Iyy = b3H/12 + B3h/12 Section modulus Sxx = Ixx/yc Section modulus Syy = Iyy/xc Centroid distance xc = B/2 Centroid distance yc= [(H+h/2)hB+H2b/2]/A
 Hollow Circle Section Modulus Formula Parameter Equation Area moment of inertia Ixx = πd4/64 - πd14/64 Area moment of inertia Iyy = πd4/64 - πd14/64 Section modulus Sxx = 2Ixx/d Section modulus Syy = 2Iyy/d
 Round Bar Section Modulus Formula Parameter Equation Area moment of inertia Ixx = πd4/64 Area moment of inertia Iyy = πd4/64 Section modulus Sxx = 2Ixx/d Section modulus Syy = 2Iyy/d
 Angle with Unequal Legs Section Modulus Formula Symbol Equation Area moment of inertia Ixx = 1/3*[bd3 - (b-t) * (d-t)3] - A * (d - yc)2 Area moment of inertia Iyy = 1/3*[db3 - (d-t) * (b-t)3] - A * (b - xc)2 Centroid distance xc=(b2+dt-t2)/(2*(b+d-t)) Centroid distance yc=(d2+bt-t2)/(2*(b+d-t)) Minimum section modulus Sxx,min=Ixx/(d-yc) Minimum section modulus Syy,min=Iyy/(b-xc)

### Reference:

• Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2016) . Machinery's Handbook . 30th edition.  Industrial Press Inc.
• Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2012) . Machinery's Handbook . 29th edition.  Industrial Press Inc.