Structural Steel Design / module 6
Cross-section resistance
What a slice of steel can carry — in tension, compression, bending, shear and torsion, and in the combinations that actually occur.
What you will understand
- Distinguish gross yielding from net-section fracture, and say why it matters
- Calculate block tearing, and explain why it mixes a yield term with an ultimate term
- Apply the section class to choose the right modulus
- Derive the plastic shear resistance and say which part of it is code
- Derive the N–M interaction of a rectangle, and see why an I section differs
- Explain why an open section is so poor in torsion, and when warping takes over
Lessons
Tension, compression, and the holes you drilled
A tension member is the simplest thing in structural steel, right up to the point where you connect it.
Bending, shear, and what happens when they combine
One interaction in this subject falls out of mechanics. Every other one is fitted — and knowing which is which changes how much you trust them.
Module summary
- Yielding is ductile and uses fy on the gross area; fracture is brittle and uses fu on the net
- In S355 about 15% of the area may be lost to holes before fracture governs
- What decides that is the yield ratio fu/fy, not the grade number
- Block tearing adds a FRACTURING tension face to YIELDING shear faces
- τy = fy/√3 is derived from von Mises; the shear AREA is the simplification
- Shear reduces bending only above 0.5 Vpl — a few percent at moderate shear, a third at full shear
- For a rectangle, m = 1 − n² exactly — the one interaction that is derivable
- An I section is flatter at low axial load, because the web carries the axial force
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesCheck your understanding
Practice
A 6000 mm² tie in S355 has 5200 mm² net area. What is the gross yielding resistance, in kN? Take γM0 = 1.0.
Practice
For that same tie, what is the net fracture resistance, in kN? Take fu = 510, γM2 = 1.25.
Practice
A block has Ant = 750 mm² and Anv = 1800 mm², in S275 (fy = 275, fu = 430). What is the block tearing resistance, in kN?
Practice
A rectangular section carries 60% of its squash load. What fraction of its plastic moment remains?
Practice
A section has Wpl = 2000 × 10³ mm³ and Wel = 1750 × 10³ mm³. By what percentage does its bending resistance fall if it drops from Class 2 to Class 3?
Practice
What is the shear yield stress of S460 steel, in N/mm², on the von Mises criterion?