span (engineering)

{{Short description|Distance between supports of an arch, bridge, etc.}}

{{One source|date=March 2023}}

{{redirect|Clear span|type of steel building|Steel building#Types}}

In engineering, span is the distance between two adjacent structural supports (e.g., two piers) of a structural member (e.g., a beam). Span is measured in the horizontal direction either between the faces of the supports (clear span) or between the centers of the bearing surfaces (effective span):{{sfn | Brett | 2012 | p=137}}

File:span definitions.png

A span can be closed by a solid beam or by a rope. The first kind is used for bridges, the second one for power lines, overhead telecommunication lines, some type of antennas or for aerial tramways.{{cn|date=December 2023}}

Image:Bending.svg beam (top) bending under an evenly distributed load (bottom).]]

Span is a significant factor in finding the strength and size of a beam as it determines the maximum bending moment and deflection. The maximum bending moment $M\_\{max\}$ and deflection $\backslash delta\_\{max\}$in the pictured beam is found using:{{Cite book |last1=Gere |first1=James M. |url=https://archive.org/details/mechanicsofmater00jame |title=Mechanics of Materials |last2=Goodno |first2=Barry J. |date=2001 |isbn=978-1-111-57773-5 |edition=Eighth |page=1086 |publisher=Cengage Learning |url-access=registration}}

:$M\_\{max\}\; =\; \backslash frac\; \{q\; L^2\}\; \{8\}$

:$\backslash delta\_\{max\}\; =\; \backslash frac\; \{5\; M\_\{max\}\; L^2\}\; \{48\; E\; I\}\; =\; \backslash frac\; \{5\; q\; L^4\}\; \{384\; E\; I\}$

where

:$q$ = Uniformly distributed load

:$L$ = Length of the beam between two supports (span)

:$E$ = Modulus of elasticity

:$I$ = Area moment of inertia

The maximum bending moment and deflection occur midway between the two supports. From this it follows that if the span is doubled, the maximum moment (and with it the stress) will quadruple, and deflection will increase by a factor of sixteen.