STRUCTURAL

Radius of Gyration

√(I/A): distributes a section's area for buckling/slenderness calculation

Also calledr valuerminleast radius of gyration
Related on InfraLens
CODES
IS 800
Definition

The radius of gyration r = √(I/A) is the distance from the neutral axis at which the whole cross-sectional area could be concentrated to give the same moment of inertia. It links a section's geometry to its buckling resistance: the slenderness ratio of a compression member is its effective length divided by its least radius of gyration (KL/rmin), and buckling always occurs about the axis of least r.

It is read directly from IS 808 steel-section tables (rxx and ryy) or computed for built-up/composite sections. Efficient columns maximise the least r for a given area — which is why tubular and box sections (similar r about both axes) outperform I-sections (small ryy) as columns. In RCC it appears in slender-column checks; for circular columns r = D/4, for rectangular r = b/√12 about the weaker axis.

Where used
  • Column/strut slenderness ratio (KL/rmin)
  • Steel-section selection from IS 808 tables
  • Built-up + laced/battened column design
  • Choosing efficient compression-member shapes
  • Slender RCC column checks (IS 456)
Acceptance / threshold
Used to compute KL/rmin which must satisfy IS 800 slenderness limits (≤180 main, ≤250 bracing) or IS 456 short/slender-column classification.
Frequently asked
How is radius of gyration calculated?
r = √(I/A), where I is the second moment of area about the relevant axis and A is the cross-sectional area. The least value (rmin) governs buckling.
Why do tubular columns perform better than I-sections?
A tube has a similar, large radius of gyration about both axes, so it resists buckling equally in all directions for a given area; an I-section has a much smaller r about its weak axis, governing its column capacity.
Related terms
Slenderness Ratio
Effective length ÷ radius of gyration; decides column buckling behaviour
Buckling / Slenderness
Compression member instability under axial load
Moment of Inertia (Second Moment of Area)
Geometric property quantifying a section's resistance to bending
Composite Beam (Steel-Concrete)
Steel beam + concrete slab made to act as one section via shear connectors
Effective Length of Column
Equivalent pin-ended length of a column for buckling, set by end restraint
Section Modulus
Section property relating bending moment to extreme-fibre bending stress
P-Delta Effect
Secondary moments due to axial load × lateral deflection
Beam Design (RCC/Steel)
Flexure + shear design per IS 456 (RCC) or IS 800 (steel)
Truss Design
Steel truss for roofs/bridges per IS 800
Influence Line
Graph of a response at one point as a unit load moves across the structure