Title 5.2 Analysis of Determinate Beams_Area-Moment.pdf ✅

Structural Theory CE321-LEC-T Lecture 5: Analysis of Determinate Beams
TECHNOLOGICAL UNIVERSITY OF THE PHILIPPINES-TAGUIG Km. 14 East Service Rd. Western Bicutan Taguig City CE236-236L-T Prepared by: Engr. JBS Objectives • Discuss the concept of deflection • Discuss the methods in determining deflections for determinate beams ❖ Double Integration Method ❖ Area – moment theorem ❖ Conjugate Beam Method ❖ Three-Moment Equation
CE236-236L-T AREA-MOMENT THEOREMS The initial ideas for the two moment-area theorems were developed by Otto Mohr and later stated formally by Charles E. Greene in 1873. These theorems provide a semi-graphical technique for determining the slope of the elastic curve and its deflection due to bending. They are particularly advantageous when used to solve problems involving beams, especially those subjected to a series of concentrated loadings or having segments with different moments of inertia. A useful and simple method of determining slopes and deflections in beams involves the area of the moment diagram and the moment of that area – the area moment method. The method is especially useful in directly determining the slope or deflection at a specified position.
CE236-236L-T AREA-MOMENT THEOREMS To develop the theorems, reference is made to the beam shown. If we draw the moment diagram for the beam and then divide it by the flexural rigidity, EI, the “M/EI diagram” . Thus it can be seen that the change in the slope of the tangents on either side of the element dx is equal to the lighter-shaded area under the M/EI diagram. Integrating from point A on the elastic curve to point B, θB/A = න A B M EI dx This equation forms the basis for first moment- area theorem. (Eq. 1)