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Beams are structural members loaded at right angles (perpendicular) to their length Most beams are horizontal and subjected to gravity or vertical loads, e g a shelf support However a vertical member can act as a beam under certain conditions, such as a curtain wall mullion subjected to wind loading The bending moment developed in a beam is dependent on:
(a) The amount of load applied, (b) The type of loading applied, (c) The support conditions
Beam Loading - Point Load
A load concentrated onto a very small length of the beam is a point load
Beam Loading - Uniform Load
A load spread evenly over a relatively long length of the beam is a uniform load
Point and uniform loads can be placed on a beam in any combination A series of point loads can approximate a uniform loading The load charts and tables are based on a uniform load unless identified otherwise
Support Conditions - Simple Beam
A simple beam has supports that prevent movement left and right, or
up and down, but do not restrain the beam from rotating at the supports into a natural deflected curve most connections produce simple beams The load charts and tables are based on simple beams unless identified otherwise
Support Conditions - Continuous Beam
Any simple beam that is supported at one or more intermediate points is a continuous beam A mezzanine joist that passes over three or more columns is an example of a continuous beam
Support Conditions - Fixed-End Beam
Supports that prevent the beam from rotating into a natural deflected curve produce a fixed-end beam A welded end connection to very rigid support produces a fixed-end beam
Support Conditions - Cantilever Beam
A cantilever beam is a fixed-end beam that is supported at one end only, while the other end is unsupported brackets are examples of cantilever beams
Deflection
All beams deflect under load The amount of deflection is dependent on (a) the amount of load,
(b) the support conditions,
(c) the stiffness of the beam’s cross-sectional shape,
(d) the stiffness of the beam material
The stiffness of the beam’s cross-sectional shape is measured by its “Moment Of Inertia” or "I" The larger a beam’s "I", the stiffer it is and the less it will deflect A beam’s "I" can change for each major axis The "I" of both major axes (I 1-1 and I 2-2) are provided
The stiffness of a beam’s material is measured by its “Modulus of Elasticity” or "E" The larger a material’s "E", the stiffer it is and the less it deflects For example, steel is about three times stiffer than aluminum and as a result, deflects only one-third as much Do not confuse stiffness with strength Two materials may have identical strengths yet still have different "E’s" A high-strength aluminum may be as strong as steel and still deflect three times as much
The load charts and tables give calculated deflections for the loads shown In many cases, a final design will be determined by the maximum deflection, not the maximum load
Bending Moment
A beam must not only hold up the anticipated loads, but must also have sufficient additional capacity to safely hold unforeseen variations in applied loads and material strengths This additional capacity is called a safety factor and is usually regulated by the various design codes and standards A beam’s strength is usually measured by an allowable bending moment or an allowable stress The traditional approach is the allowable stress method, where a beam is determined to have a maximum allowable stress (in pounds per square inch) which is not to be exceeded
The approach of the current AISI “Specification For The Design Of Cold-Formed Steel Structural Members” is to use a maximum allowable bending moment (in inch-pounds) which is not to be exceeded Bending moment divided by a beam’s section modulus or "S" equals stress
Beam - Design Fundamentals
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