The unknown displacement and slope to be determined should be indicated on the curve. Procedure for analysis Elastic curve An inflection pt or change in curvature occurs when the moment if the beam (or M/EI) is zero. Realize that when the beam is subjected to a +ve moment, the beam bends concave up, whereas -ve moment bends the beam concave down.ħ *12.4 SLOPE & DISPLACEMENT BY THE MOMENT-AREA METHOD If it is difficult to draw the general shape of the elastic curve, use the moment (M/EI) diagram. Recall that pts of zero slope and zero displacement always occur at a fixed support, and zero displacement occurs at all pin and roller supports. Procedure for analysis Elastic curve Draw an exaggerated view of the beam’s elastic curve.
MOMENT AREA THEOREM STRUCTURAL ANALYSIS EXAMPLES SERIES
If the loading consists of a series of distributed loads, the M/EI diagram will consist of parabolic or perhaps higher-order curves, and we use the table on the inside front cover to locate the area and centroid under each curve.Ħ *12.4 SLOPE & DISPLACEMENT BY THE MOMENT-AREA METHOD If the beam is loaded with concentrated forces, the M/EI diagram will consist of a series of straight line segments, and the areas and their moments required for the moment-area theorems will be relatively easy to compute. Procedure for analysis M/EI Diagram Determine the support reactions and draw the beam’s M/EI diagram. This moment is computed about pt (A) where the vertical deviation (tA/B) is to be determined.Ĥ *12.4 SLOPE & DISPLACEMENT BY THE MOMENT-AREA METHODĥ *12.4 SLOPE & DISPLACEMENT BY THE MOMENT-AREA METHOD the tangent extended from another pt (B) equals the moment of the area under the ME/I diagram between these two pts (A and B). Theorem 2 The vertical deviation of the tangent at a pt (A) on the elastic curve w.r.t. Theorem 1 The angle between the tangents at any two pts on the elastic curve equals the area under the M/EI diagram between these two pts.Ģ *12.4 SLOPE & DISPLACEMENT BY THE MOMENT-AREA METHODģ *12.4 SLOPE & DISPLACEMENT BY THE MOMENT-AREA METHOD
Presentation on theme: "*12.4 SLOPE & DISPLACEMENT BY THE MOMENT-AREA METHOD"- Presentation transcript:ġ *12.4 SLOPE & DISPLACEMENT BY THE MOMENT-AREA METHODĪssumptions: beam is initially straight, is elastically deformed by the loads, such that the slope and deflection of the elastic curve are very small, and deformations are caused by bending.