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Beam - Design Fundamentals

            Beams are structural members loaded at right angles (perpendicular) to   Deflection
            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,
                                                                  All beams deflect under load The amount of deflection is dependent on
               (b) The type of loading applied,
                                                                    (a) the amount of load,
               (c) The support conditions
                                                                    (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
            Beam Loading - Point Load                             less it will deflect A beam’s "I" can change for each major axis The "I" of
            A load concentrated onto a very small length of the beam is a point load  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
            Beam Loading - Uniform Load                           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
            A load spread evenly over a relatively long length of the beam is a   "E’s" A high-strength aluminum may be as strong as steel and still deflect
            uniform load                                          three times as much
            Point and uniform loads can be placed on a beam in any combination A   The load charts and tables give calculated deflections for the loads
            series of point loads can approximate a uniform loading The load charts   shown In many cases, a final design will be determined by the maximum
            and tables are based on a uniform load unless identified otherwise  deflection, not the maximum load

            Support Conditions - Simple Beam                      Bending Moment
            A simple beam has supports that prevent movement left and right, or   A beam must not only hold up the anticipated loads, but must also have
            up and down, but do not restrain the beam from rotating at the supports   sufficient additional capacity to safely hold unforeseen variations in
            into a natural deflected curve most connections produce simple beams   applied loads and material strengths This additional capacity is called a
            The load charts and tables are based on simple beams unless identified   safety factor and is usually regulated by the various design codes and
            otherwise                                             standards A beam’s strength is usually measured by an allowable bending
                                                                  moment or an allowable stress The traditional approach is the allowable
            Support Conditions - Continuous Beam                  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
            Any simple beam that is supported at one or more intermediate points   moment divided by a beam’s section modulus or "S" equals stress
            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

            ZSi-Foster Engineering Catalog                                                                    – 5 –
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