Structural Engineering

Steel — Tension & Compression Members

IS 800 limit-state design: gross-section yielding, slenderness and the fundamentals of member capacity.

PART 1

Topic Breakdown & Traps

The Engineering Principle

A tension member can fail by gross-section yielding, net-section rupture or block shear; the design strength is the least of these. A compression member's capacity falls as its slenderness ratio

λ = L_{e} / r_{min}

rises (Euler buckling). Effective length depends on end conditions.

The Core Formula Matrix

Gross-section yielding:

T_{d g} = \frac{A _{g} f _{y}}{γ _{m 0}}

γ_{m 0} = 1.10

.

Slenderness ratio:

λ = \frac{L _{e}}{r _{min}}

Euler critical load:

P_{cr} = \frac{π ^{2} E I}{L _{e}^{2}}

Effective length factors: both fixed →

0.65 L

, both pinned →

1.0 L

, fixed-free →

2.0 L

.

Fillet weld throat:

t = 0.707 s

The ‘IIT Traps’

⚠
Least of three limit states. Tension design uses the minimum of yielding, rupture and block shear.
⚠
** $r_{min}$ , not $r_{ma x}$ .** Buckling occurs about the weakest axis.
⚠
Effective length ≠ actual length. Apply the end-condition factor.

📚 Standard references

Limit State Design of Steel Structures — S.K. Duggal
IS 800:2007 — General Construction in Steel — Bureau of Indian Standards

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · NAT

A column has effective length

4000 mm

and minimum radius of gyration

40 mm

. Its slenderness ratio is _____.

Q2MEDIUM2 Marks · NAT

A tension member of gross area

1500 mm^{2}

(Fe250,

γ_{m 0} = 1.1

) has gross-yielding strength _____ kN.

Q3HARD1 Mark · MCQ

For a column with both ends fixed (no sway), the theoretical effective length factor is: