J-01 — reading a deflected shape

the curve tells you where the beam wants to go.

deflected shape viewer

change the supports. watch the shape change.

See how a beam deflects under load and learn to read the engineering diagram that describes it.

support condition
loading
w (k/ft) 2.0
depth 18 in
span 24 ft
—
max deflection
at midspan
live equation
—
Δ = Largest vertical displacement along the beam
L = Distance between supports
E = Material stiffness
I = Section property resisting bending
explained
The deflection formula shows that span length dominates — L appears to the fourth power. Doubling the span increases deflection 16-fold. Increasing beam depth helps because I is proportional to d cubed. These relationships explain why long-span beams are always deep.
key concepts
what it shows The deflected shape is the beam's displaced position, exaggerated

In reality, beam deflections are tiny compared to the span — fractions of an inch over 20+ feet. The diagram exaggerates the vertical scale so you can see the shape. The curve shows how far each point along the beam moves vertically under load.

support conditions The supports define where the deflection is zero

At a pin or roller, vertical displacement is zero — the curve is pinned to the baseline. At a fixed end, both displacement AND slope are zero — the curve leaves the support horizontally. A free end (cantilever tip) has the maximum displacement. Understanding the boundary conditions tells you the shape before you calculate anything.

why it matters Deflection limits protect what's attached to the structure

Codes limit deflection to fractions of the span — L/360 for floors under live load, L/240 for total load. These limits prevent cracking of partitions, sagging of ceilings, and the uneasy feeling of a bouncy floor. A beam can be strong enough to not break and still deflect too much to be usable.