How Calculations Regarding Section Modulus Determine Steel Bending

When determining whether a given steel section can be curved without heat, it is useful to determine its section modulus and relate that value to the strength of the steel bending equipment.

Section modulus measures the flexural strength of a given section of steel.   More specifically, 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 because this is where the material will yield first.   The units for section modulus are typically cubic inches / in^3 / in3. The bending moment that it takes to yield that section equals the section modulus times the yield strength.

Various bending equipment has section modulus ratings.  For example, a three-roll section bender that can bend a 3 x 3 x 3/8 angle and comparable steel bars, beams, channels, tees, pipe and tube would have a section modulus of approximately 1.2 in3.  So given the requirement to bend a certain steel section, if the calculation of the section modulus of a given steel section (either mathematically or by reference to  engineering tables) yields a value in cubic inches that equals or is less that the calculated strength of the bending machine, then the machine should be able to curve the section.  One caveat, however, is that more power may be needed for tight radius bends.

Three-roll section benders are available with section modulus ratings from 0.4 in3 to 500 in3 and beyond (for special applications.)

After the determination is made as to whether a given section bender can curve a given steel section, it needs to be determined if the section can be bent with the quality requisite for the application.  AESS (Architecturally Exposed Structural Steel) concerns might dictate that the steel sections have virtually no distortion or even scratches on the surface of the steel.  For example, if the exposed curved steel section appears only a few feet above travelers’ heads as they ride an escalator in an airport, it will have to be near perfect. Similarly, parts for OEMs (original equipment manufacturers) might require curved sections which meet very high dimensional and appearance standards.  Even though the tractor will no doubt not be like a shiny new car once it is put into service, the farmer wants to see it that way when he buys it.

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