# I BEAM DESIGN FOR STRENGTH

I Beam Strength Calculator has been developed to calculate normal stress, shear stress and Von Mises stress at critical points of a given cross section of a beam.

The transverse loading on a I Beam may result normal and shear stresses simultaneously on any transverse cross section of the I beam. The normal stress on a given cross section changes with respect to distance y from the neutral axis and it is largest at the farthest point from the neural axis. The normal stress also depends on the bending moment in the section and the maximum value of normal stress in I beam occurs where the bending moment is largest. Maximum shear stress occurs on the neutral axis of the I beam where shear force is maximum.

Note: For more information on the subject, please refer to "Shearing Stresses in Thin-Walled Members" and "Design of Beams and Shafts for Strength" chapters of Mechanics of Materials .

##### Calculator:

 INPUT PARAMETERS Parameter Symbol Value Unit Structural Beam Height 2c mm cm m inch ft Structural Beam Width w I Beam Flange Thickness t1 I Beam Web Thickness t2 Shear Force V kN N lbf Bending Moment M N*m kN*m lbf*in lbf*ft

###### Note: Structural beam is assumed to be subjected a vertical shearing force in its vertical plane of symmetry.

 OUTPUT PARAMETERS Parameter Symbol Value Unit Cross section area A --- mm^2 cm^2 inch^2 ft^2 First moment of area for section A QA --- mm^3 cm^3 inch^3 ft^3 First moment of area for Section B QB --- First moment of area for section D QD --- Second moment of area Izz --- mm^4 cm^4 inch^4 ft^4 Stress Calculation at Section A MPa psi ksi Normal stress σx_A --- Shear stress τxy_A --- Von Mises stress at A σv_A --- Stress Calculation at Section B Normal stress at B σx_B --- Shear stress at B τxy_B --- Von Mises stress at B σv_B --- Stress Calculation at Section D Normal stress at D σx_D --- Shear stress at D τxy_D --- Von Mises stress at D σv_D ---

##### Definitions:

I Beam: I beam is a type of beam often used in trusses in buildings. I beam is generally manufactured from structural steels with hot and cold rolling or welding processes. Top and bottom plates of a I beam are named as flanges and the vertical plate which connects the flanges is named as web.

Normal Stress: Stress acts perpendicular to the surface (cross section).

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

Shear stress: A form of a stress acts parallel to the surface (cross section) which has a cutting nature.

Stress: Average force per unit area which results strain of material.

##### Supplements:

 Link Usage Structural beam deflection and stress calculators Calculates parameters of the compression member (column) for different end conditions and loading types. Calculators also covers bending moment, shear force, bending stress, deflections and slopes calculations of simply supported and cantilever structural beams for different loading conditions. Sectional Properties Calculator of Profiles Sectional properties needed for the structural beam stress analysis can be calculated with sectional properties calculator.

##### List of Equations:

 Parameter/Condition Symbol Equation Cross section area A A = 2t1w+2(c-t1)t2 Area moment of inertia Izz Izz = (2c-2t1)3t2/12 + 2[t13w/12 + t1w((2c-2t1)+t1)2/4] Normal stress σx σx=My/I Shear stress τxy τxy=(VQ)/(Ib) First moment of area for section B QB QB=w*t1*(c-t1/2) First moment of area for section C QD QD=w*t1*(c-t1/2)+(t2*(c-t1)2)/2 Thickness b for section B and C b b=t2 Von Mises Stress σv

##### Reference:
• Beer.F.P. , Johnston.E.R. (1992). Mechanics of Materials , 2nd edition. McGraw-Hill, Chapter 5.9 and Chapter 7.6