Steel Deflection Calculator

Formula

The formula to calculate the deflection of a steel beam is:

\[ \delta = \frac{5 W L^4}{384 E I} \]

Where:

\(\delta\) is the deflection of the beam (inches)
\(W\) is the load on the beam (pounds)
\(L\) is the length of the beam (inches)
\(E\) is the modulus of elasticity of the steel (psi)
\(I\) is the moment of inertia of the beam's cross section (in^4)

What is Steel Deflection?

Steel deflection refers to the degree to which a structural element is displaced under a load. It may occur in beams, columns, or trusses due to forces such as wind, gravity, seismic activity, or even the weight of occupants and furniture. The amount of deflection in a steel structure is a crucial factor in its design as excessive deflection can lead to structural failure or damage to attached materials.

Example Calculations

Example 1:

Load on the Beam (W) = 1000 pounds
Length of the Beam (L) = 120 inches
Modulus of Elasticity (E) = 29000 psi
Moment of Inertia (I) = 50 in^4

Using the formula:

\[ \delta = \frac{5 \times 1000 \times 120^4}{384 \times 29000 \times 50} = 1832 \, \text{inches} \]

The deflection of the beam (δ) is 1862 inches.

Example 2:

Load on the Beam (W) = 500 pounds
Length of the Beam (L) = 60 inches
Modulus of Elasticity (E) = 29000 psi
Moment of Inertia (I) = 30 in^4

Using the formula:

\[ \delta = \frac{5 \times 500 \times 60^4}{384 \times 29000 \times 30} = 96.98 \, \text{inches} \]

The deflection of the beam (δ) is 96.98 inches.