The student of any technical college faces creation of an epyur at the very beginning of the way to the higher education. And it does it on two objects: descriptive geometry and resistance of materials. On the first, under epyury mean Epur Monge, that is a projection of a three-dimensional object to three orthogonal planes. On the second — the schedule of change of the loadings attached to a beam on its length.
It is required to you
- notebook;
- handle;
Instruction
1. Any three-dimensional figure can be focused rather rectangular system of coordinates. Such system turns out when crossing three planes perpendicular each other. It is accepted to designate these planes as horizontal, frontal and profile. Epur Monge represents the flat drawing on which the frontal and horizontal planes are combined with frontal, and an object, epyur who needs to be constructed, orthogonally is projected on all three planes. Thus epyur Monge represents plane model of a three-dimensional object. To construct an orthogonal projection of some point to the plane carry out from it the projecting beam on this plane. Having projected all significant points of an object on three planes, you receive required epyur.
2. To construct epyur the bending moments, cross and longitudinal forces, it is necessary to perform a number of consecutive operations. Define a type of the considered object. In standard tasks in study of the strength of materials beams, frames and farms meet. Define types of communications of an object, an object can have a rigid support, a mobile support and tough seal. Depending on a type of communications various number of reactions are formed. At tough seal there are reactions along axes and torque. At a rigid support there are reactions along axes. At a mobile support there is only one reaction parallel to a support core. After you defined types of reactions, apply them on the drawing. Now you need to find quantitative expression of reactions of support. For this purpose it is necessary to work out the equations proceeding from the fact that the sum of forces and reactions operating on an object is equal to zero, both the sum of the moments caused by forces and reactions is equal to zero. The moments of forces are equal to the work of these forces on a shoulder. It is necessary to work out the balance equations for two axes and the moments, the system from three equations which will allow to find required sizes of reactions of support as a result will turn out. Construction epyur comes down to creation of the schedule of changes of the moments and loadings on axis x. Loading on any site is on formula Q = q*x+Q0. Where q is the distributed loading on the site, and Q0 is loading at the beginning of the site. The moment on any site is on formula M = (q*x^2)/2 + Q0*x + M0. Having broken a beam into sites and having calculated the moments and loadings for the ends of sites you will be able to construct the schedule of their change, i.e. epyur.