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Cantilever, partially distributed load — Square

Deflection and stress of a beam. Section: Square. Load case: Cantilever, partially distributed load.

Diagram: Cantilever, partially distributed load Square
Diagram: Cantilever, partially distributed load Square

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Input

Beam length
LL
Loaded length
l1l_1
Young's modulus
EE
Side length
aa
Density
ρρ
Acceleration due to gravity
gg

Result

Beam mass
mm
Distributed load from the beam's self-weight
ww
Second moment of area
II
Section modulus
ZZ
Reaction force
RR
Maximum bending moment
MM
Maximum deflection
δ\delta
Maximum bending stress
σ\sigma
  • The following is from 8.1 "Deflection of beams" of the AIJ Standard for Allowable Stress Design of Steel Structures (2019).
    • Under long-term loading, the deflection of a beam shall not exceed 1/300 of the span, or 1/250 for a cantilever. Purlins, girts and the like may go beyond this limit so long as the finish is not affected.
    • Where live load acts dynamically, the resulting vibration of the beam shall be checked so that comfort, the operation of precision equipment and productivity are not impaired.
    • For crane runway girders the limit is 1/500 of the span for hand-operated cranes, and 1/800 to 1/1 200 for other electric cranes, according to the circumstances.
Cantilever Beam, Square Section — Deflection Calculator | Updraft - Mechanical Engineering Calculators