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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): [1] A span can be closed by a solid beam or by ...
Shear and Bending moment diagram for a simply supported beam with a concentrated load at mid-span. Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam.
Figure 1: (a) This simple supported beam is shown with a unit load placed a distance x from the left end. Its influence lines for four different functions: (b) the reaction at the left support (denoted A), (c) the reaction at the right support (denoted C), (d) one for shear at a point B along the beam, and (e) one for moment also at point B. Figure 2: The change in Bending Moment in a ...
L is the length of the support (outer) span; b is width; d is thickness; For the 4 pt bend setup, if the loading span is 1/2 of the support span (i.e. L i = 1/2 L in Fig. 4): = If the loading span is neither 1/3 nor 1/2 the support span for the 4 pt bend setup (Fig. 4): Fig. 4 - Beam under 4 point bending
l A: Span length (distance between support point and the nearest loading point of the test punch) in mm; l B: Length of the reference beam (between the loading points, symmetrically placed relative to the loading points) in mm; D L: Distance between the reference beam and the main beam (centered between the loading points) in mm
The deflection at any point, , along the span of a center loaded simply supported beam can be calculated using: [1] = for The special case of elastic deflection at the midpoint C of a beam, loaded at its center, supported by two simple supports is then given by: [ 1 ] δ C = F L 3 48 E I {\displaystyle \delta _{C}={\frac {FL^{3}}{48EI}}} where
Other beams can have both ends fixed (known as encastre beam); therefore each end support has both bending moments and shear reaction loads. Beams can also have one end fixed and one end simply supported. The simplest type of beam is the cantilever, which is fixed at one end and is free at the other end (neither simple nor fixed). In reality ...
Simply supported beam with a single eccentric concentrated load. An illustration of the Macaulay method considers a simply supported beam with a single eccentric concentrated load as shown in the adjacent figure. The first step is to find . The reactions at the supports A and C are determined from the balance of forces and moments as