Guide
1
Draw a design scheme, which is a schematic representation of the beam, its supports and their reactions, as well as the impact load.An example of a design scheme is shown in Figure 1.
2
Reactions supports are put in view of the fact that the pivotally movable support-cross reaction occurs only in the hinge-fixed support - longitudinal and transverse reaction in rigid clamping -both types of reactions and reactive moment.Vybirat support reactions can be arbitrary, if as a result of further settlements will turn negative some of the reactions, it means you have to change napravlenie.Posle how you decide the kinds of supports and put down their reactions, it is necessary to break the beamportions, assumi
ng that the section should not be modified acting forces.
3
Now you need to create the equilibrium equations for the x and y axes and moments acting .To do this, you must know that the sum of all the moments , acting on the beam is zero, and the sum of all the forces of the axes is zero.If the beam acts of load distribution, when the equations of equilibrium it must be replaced by a concentrated force, which will be equal to the product of the load distribution on the length of the plot on which it operates.Using the system of three equations of equilibrium, determine the reactions of the supports.
4
now calculate the value of the longitudinal forces and bending moments at each site.To do this, use the following formulas: lateral load Q = q * x + Q0, where Q0 - the sum of forces from all the previous sections, q - distributed load on the site, x - length of the section.The bending moment Mi = (q * x ^ 2) / 2 + Q0 * x + M0, where M0 - torque value at the beginning of the plot.
5
Now you have all the data for building diagrams, which represent a graph of the load along the length of the beam.First build epure lateral forces by the scale, noting the size of the load at the beginning of each section and connecting the data points.Now mark the bending moments on sites and connect the points, given that if the diagram of shear forces in this area is a straight line parallel to the beam, then the diagram of bending moments be inclined line, if on the diagram of shear forces - the inclined linethen on the diagram of bending moments forms a parabola.
Tip 2: How to Build a moment diagram
Scientifically diagram - a graphical representation of changes in the function of the law, depending on the variation of the argument (X).With the help of diagrams define the maximum permissible load on the material.
you need
- notebook, pen, pencil, calculator, ruler
Guide
1
determine the type of system you are considering.Most often, it may be frame or truss beam.These structures are flat or spatial core of the system, all elements of which are connected to each other in knots (hard or hinges).
2
now specify the type of fixing of the reference design (connection).The system can be pivotally movable support, hinged-fixed support and rigid clamping (termination).Number of responses (R) in the system will depend on exactly what your type of connection.For example, a pivotally-movable support there is only one reference reaction directed perpendicular to the reference plane.The hinged-fixed support, there are two reactions: vertical and horizontal.A tight sealing of even a reference (reactive) moment.
3
Calculate the support reactions.For cantilever beams support reactions resulting in tight seals, can not be calculated.For other cases, use two basic equations of statics.The sum of all forces acting on the system and responses, as well as the sum of moments (caused by these forces and reactions) should be zero.
4
Schedule specific section (broken down into sections) and identify them in the transverse forces.Be sure to build epure shear forces (Qy).With it you can check the correctness of the construction of diagrams of moments.
5
now in the same selected cross sections define the bending moments.The bending moment in a typical cross-section is determined by the following formula: Mx = R * a + (q * x ^ 2) / 2 * M0.
Where R - the reaction of the support;and - her shoulder;q - the load;
Where R - the reaction of the support;and - her shoulder;q - the load;
6
the obtained data, build diagrams of transverse forces and bending moments.Remember that the order line on the diagram Mx is always one more than the diagram Qy.For example, if the diagram Qy - oblique line, the diagram Mx in this area - a square parabola;If the diagram Qy - a line parallel to the axis, Mx diagram on this site - oblique line.
Sources:
- Sopromat online