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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 ...
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral ...
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
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
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
The moment M1, M2, and M3 be positive if they cause compression in the upper part of the beam. (sagging positive) The deflection downward positive. (Downward settlement positive) Let ABC is a continuous beam with support at A,B, and C. Then moment at A,B, and C are M1, M2, and M3, respectively.
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 ...
The beams are continuously formed, so the length of the beam is limited only to the maximum length that can be handled and transported. Typical widths are 3 + 1 ⁄ 2, 5 + 1 ⁄ 4 or 7 inches (89, 133 or 178 mm); typical depths are 9 + 1 ⁄ 2, 11 + 7 ⁄ 8, 14, 16 and 18 inches (240, 300, 360, 410 and 460 mm). Typically the beams are made to a ...