Measures how area is distributed from an axis; governs bending stiffness.
The second moment of area I=∫y²dA measures how far area lies from an axis and governs bending stiffness. Rectangle: bh³/12; circle: πd⁴/64. Depth enters cubed, so deep sections are efficient in bending.
Doubling the beam depth multiplies stiffness by eight.
The second moment of area describes how a cross-section resists bending, so it decides whether a beam is stiff enough for the load.
Measures how area is distributed from an axis; governs bending stiffness.
The second moment of area describes how a cross-section resists bending, so it decides whether a beam is stiff enough for the load.
I depends on the cube of the depth for a rectangle, so increasing depth gives far more stiffness than the same increase in width.
Length to the fourth power, such as mm to the fourth or m to the fourth.
Typical applications include comparing a square tube and a solid bar for the same weight, checking the deflection of a floor joist and choosing a steel section for a crane runway beam.
Study "Cables and arches" first (topic 18 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Units m⁴. Principal axes maximise and minimise I. Polar moment J=Ix+Iy.
Doubling the beam depth multiplies stiffness by eight.
The next topic is "Parallel axis theorem", which builds directly on this one.
It is classed as Beginner in Engineering Mechanics (topic 19 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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