IPE 100
IPE 120
IPE 140
IPE 160
IPE 180
IPE 200
IPE 220
IPE 240
IPE 270
IPE 300
HEA 100
HEA 120
HEA 140
HEA 160
HEA 180
HEA 200
HEA 220
HEA 240
HEA 260
HEA 280
HEA 300
HEB 100
HEB 120
HEB 140
HEB 160
HEB 180
HEB 200
HEB 220
HEB 240
HEB 260
HEB 280
HEB 300
Required Section Modulus (Z)
Understanding Steel Beam Strength Calculations
This Steel Beam Calculator provides an estimation of the required section modulus (Z) for a simply supported steel beam under a uniformly distributed load. The section modulus is a crucial geometric property of a beam's cross-section that indicates its resistance to bending. A higher section modulus generally means the beam can withstand greater bending stress before yielding.
How it Works:
The calculation is based on fundamental structural engineering principles for bending stress. For a simply supported beam with a uniform load, the maximum bending moment (M) occurs at the center and is calculated as:
M = (w * L^2) / 8
Where:
w is the uniformly distributed load per unit length (kN/m).
L is the beam span in meters (m).
The bending stress (σ) in the beam is related to the bending moment (M) and the section modulus (Z) by the formula:
σ = M / Z
To determine the required section modulus, we rearrange this formula. We need to consider the yield strength (fy) of the steel grade and apply a partial safety factor (γm) for materials, which is typically around 1.15 for steel structures. The design bending moment (Md) is the applied moment multiplied by a load factor (γf), commonly 1.5 for ultimate limit states. The allowable bending stress (σd) is the yield strength divided by the material safety factor (fy / γm).
The required section modulus (Z) is then calculated to ensure that the beam's resistance (Z * σd) is greater than or equal to the applied design moment (Md). A simplified approach, often used for preliminary estimations, involves determining the maximum bending moment and then finding a beam section with an adequate Section Modulus based on established design codes and material properties.
Simplified Calculation for this Tool:
This calculator simplifies the process by calculating the maximum bending moment (M) from the total applied load (W) and span (L) assuming the load is uniformly distributed: M = (W/L * L^2) / 8 = (W * L) / 8. It then uses a target allowable bending stress (σ_allowable) which is derived from the steel grade's yield strength (fy) and a typical safety factor. The required Section Modulus (Z) is then approximated by:
Z_required = (M * Safety_Factor) / fy
*Note: This is a simplified calculator for initial estimation purposes. Actual structural design must be performed by a qualified engineer using relevant building codes and detailed analysis, considering factors like shear stress, deflection, buckling, and load combinations.*
Steel Grades:
S275: A common structural steel grade with a minimum yield strength of 275 N/mm². Suitable for general construction.
S355: A higher strength steel with a minimum yield strength of 355 N/mm². Offers greater load-bearing capacity for its weight.
Beam Sections:
The calculator includes common European profiles (IPE, HEA, HEB). Each profile has specific geometric properties, including its section modulus (Z), which are looked up internally based on the selected profile.
Use Cases:
Preliminary structural design and feasibility studies.
Quick checks for selecting appropriate beam sizes in small to medium-sized projects.
Educational purposes for understanding basic structural principles.