Span (engineering)




Span is the distance between two intermediate supports for a structure, e.g. a beam or a bridge.
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.



Side view of a simply supported beam (top) bending under an evenly distributed load (bottom).


The 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 Mmax{displaystyle M_{max}}M_{{max}} and deflection δmax{displaystyle delta _{max}}delta _{{max}}in the pictured beam is found using:[1]


Mmax=qL28{displaystyle M_{max}={frac {qL^{2}}{8}}}M_{{max}}={frac {qL^{2}}{8}}

δmax=5MmaxL248EI=5qL4384EI{displaystyle delta _{max}={frac {5M_{max}L^{2}}{48EI}}={frac {5qL^{4}}{384EI}}}delta _{{max}}={frac {5M_{{max}}L^{2}}{48EI}}={frac {5qL^{4}}{384EI}}

where




q{displaystyle q}q = Uniformly distributed load


L{displaystyle L}L = Length of the beam between two supports (span)


E{displaystyle E}E = Modulus of elasticity


I{displaystyle I}I = Area moment of inertia


Note that 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.


For long-distance rope spans, used as power line, antenna or for aerial tramways, see list of spans.



References





  1. ^ Gere, James M.; Goodno, Barry J. Mechanics of Materials (Eighth ed.). p. 1086. ISBN 978-1-111-57773-5..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output q{quotes:"""""""'""'"}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-limited a,.mw-parser-output .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}









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