At impact on a beam of cross forces there are bending moments which are the main destroying factor therefore at structural design it is very important to calculate force of the bending moments on different sites. Visually to represent influence of the bending moments, build their epyura.
Instruction
1. Draw the settlement scheme which represents the schematical image of a beam, its support and their reactions and also the influencing loadings. The example of the settlement scheme is presented in figure 1.
2. Reactions of support are put taking into account that in pivotally - a mobile support there is only a cross reaction, in pivotally - a motionless support — longitudinal and cross reactions, in rigid jamming — both types of reactions and the reactive moment. It is possible to choose reactions of support randomly if as a result of further calculations the negative value some of reactions turns out, means it is necessary to change the direction. After you decide on types of support and will put down their reactions, it is necessary to break a beam into sites, proceeding from the fact that on the site operating forces should not change.
3. Now it is necessary to work out the balance equations for axes x and y and for the operating moments. For this purpose it is necessary to know that the sum of all moments operating on a beam is equal to zero, and the sum of all forces on axes is also equal to zero. If the beam is affected by the distributed loading, then by drawing up the equations of balance it needs to be replaced with the concentrated force which will be equal to the work of force of the distributed load of length of the site on which it acts. Having used a system from three equations of balance, define reactions of support.
4. Now count the size of longitudinal forces and the bending moments on each site. For this purpose use the following formulas: cross loading of Q = q*x + Q0 where Q0 is the sum of forces from all previous sites, q is the distributed loading on the site, x — site length. The bending Mi's moment = (q*x^2)/2 + Q0*x + M0 where M0 is value of the moment at the beginning of the site.
5. Now you have all data for construction epyur which represent the schedule of change of size of loading on beam length. At first construct an epyura of cross forces, having chosen scale, having noted loading size at the beginning of each site and having connected the received points. Now note sizes of the bending moments on sites and connect points, considering that if the epyura of cross forces on this site represents the straight line parallel to a beam, on an epyura of the bending moments there will be an inclined line, if on an epyura of cross forces — the inclined line, on an epyura of the bending moments the parabola is formed.