What is stiffness?
Stiffness is the resistance of a structure or member to deformation under load, for example the deflection of a beam or floor. It is part of the strength of materials. Stiffness is about how much something deforms; strength is about when it fails. A joist can be strong enough and still be too bouncy.
The main types are:
- Axial stiffness: resistance to stretching or shortening along the member (EA).
- Bending stiffness: resistance to deflection, the product of the modulus of elasticity E and the second moment of area I (EI).
- Torsional stiffness: resistance to twisting.
Stiff does not mean rigid in the sense of never moving. A structure that is too rigid to follow shrinkage, settlement or temperature changes is more likely to crack.
Rules of thumb
The depth of a rectangular section enters the second moment of area to the third power. A beam twice as deep is therefore eight times as stiff. A 50 x 150 mm board on edge is nine times as stiff as the same board laid flat.
In design, stiffness is checked against a maximum allowed deflection, expressed as a fraction of the span L, for example L/250. The limit that applies depends on the element and on the design code in force.
Application
- Set joists on edge. That gains far more stiffness than using a heavier section laid flat.
- Shorten the span. An extra support or intermediate beam reduces deflection sharply.
- Think about finishes. Tiles and plaster tolerate little movement. A floor that is strong enough but springy will crack the tiling.
- Choose the material knowingly. Steel has a much higher modulus of elasticity than timber, so for the same section it deflects far less.
Common mistake: looking only at strength. A floor that does not break but noticeably bounces or vibrates is still unfit for use.
Related terms
- Modulus of elasticity
- Elastic deformation
- Structural stability
- Beam
- Moment
- Bending moment diagram
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