Able to analyze determinate beam deflection and slope by macaulay method. It is essentially modified method of double integration of the b. In this method, the area of the bending moment diagrams is utilized for computing the slope and or deflections at particular points along the axis of the beam or. A cantilever beam is 4 m long and has a point load of 5 kn at the free end. In this lesson, slopedeflection equations are derived considering the rotation of beam axis. If we let k be very large relative to eil3, we approach a beam pinned at. Determine the moment at each joint of the gable frame.
Macaulays method the double integration method is a technique used in structural analysis to determine the deflection of eulerbernoulli beams. Substituting x 0 into 2c and 2d gives the standard equations. Usually, before the slope and deflection are calculated, it. Macaulay recognized this fact and proposed a method which is known as the macaulays method to obtain the slope and deflection equations. Before macaulays paper of 1919, the equation for the deflection of beams could not be found in closed form. Calculation of slope and deflection by macaulays method. A geometric method uses the strain of an elastic structure to. The roof load is transmitted to each of the purlins over simply supported sections of the roof decking. Use macaulays method to determine the values of slope and deflection at 2m from the free end of the cantilever due to the imposed load as shown in figure 61a.
Differential equation for elastic curve of a beam will also be used in macaulay s method to determine the deflection and slope of the loaded beam and hence we must have to recall here the differential equation for elastic curve of a beam. Supports which resist a moment, such as a fixed end support, resist displacement and rotation or slope. The main point of interest is the slope and deflection at the free end where x0. Macaulays method is a means to find the equation that describes the deflected shape of a beam. Mechanics of materials chapter 6 deflection of beams. The beam crosssection is tshaped with flange width as 150 mm and flange thickness 10 mm. Determine the deflection of statically determinate beam by using double integration method. Slope deflection method examples purdue engineering. This is the slope of the deflected neutral axis as a function of x, at least within. Determine the deflection of statically determinate beam by using macaulay s method. In statically indeterminate structures, the beam axis rotates due to. The material of beam has modulus of elasticity as 200 gpa.
610 850 1280 1354 196 365 965 1036 1028 484 255 1395 261 871 1546 602 1549 335 1100 996 772 1019 843 113 1130 994 853 1147 71 454 1021 969 1598 1292 906 87 554 522 322 124 730 399 344 938 531