Concentrated force calculation couple

1.

In theoretical mechanics, Q stands for the action density of uniform load, which means the uniform load within the action range. The calculation method is as follows:

1. The uniform load can be equivalent to the force by integral method, and its size is equal to the area of uniform load, and the action point falls at 1 / 3 of the length near the bottom according to the moment equivalent method

2. Mechanics of materials, edited by Liu Hongwen or sun Xunfang,
in the concentrated force and concentrated couple, take a micro section with the action point of concentrated force and concentrated couple as the center,
the bending moment on both sides of the action point of concentrated force is equal, and the shear difference is the size of concentrated force
the shear force on both sides of the action point of the concentrated couple is equal, and the moment difference is the size of the concentrated couple
the bearing is similar, but the reaction force of the bearing is calculated as a concentrated force or a concentrated couple.

3.

Couple is a physical term. A pair of parallel forces with equal size, opposite direction but not collinear acting on the same rigid body is called couple. Under the action of concentrated couple, the shear diagram does not change. A concentrated couple is a couple acting on a certain section of a beam when its length is far less than the length of the beam

a pair of forces with the same size and opposite direction, but the action lines are not on the same straight line (such as F and f 'in the figure). The couple can make the object proce pure rotation effect. For example, if the tap is used with both hands, the applied couple will not proce lateral pressure on the tap, so that the drilled hole can be perpendicular to the surface. The sum of the moments of the two forces of the couple to any point in space is a constant, which is called the moment of the couple. It can be proved by statics axiom and geometry that a couple can be replaced by another couple which is parallel to its action surface and equal to its moment, without changing its rotational action on the rigid body

e to the directivity of the action plane of the couple, a moment vector t of the spatial couple should be introced, whose direction line is perpendicular to the action plane of the couple, and its direction should be determined according to the right-hand screw rule (see Figure). The magnitude of T is equal to the proct of the force and the arm of the couple (the vertical distance between the two force lines of the couple). Because the action surface of the couple can translate freely on the rigid body, the moment vector of the couple on the rigid body is a free vector, that is, its action point can be any point on the rigid body

if the couple acts on the deformed body, the moment vector of the couple can not be translated freely, because it will proce different torsion effects. An object under the action of a couple will proce angular acceleration, which cannot be balanced by a single force, because a force has a principal vector, but the principal moment of a force system composed of a couple is not zero, but the principal vector is zero. The dimension and unit of couple moment are the same as that of moment

4. Concentrated force (KN)
uniform load (KN / M)
moment and couple (kn. M)

5. Both the concentrated force and the concentrated couple are theoretical models, which are actually distributed on the infinitesimal elements and are related to the position s, which can be expressed as f (s)
the location of the support is a boundary condition problem
you can learn to use differential equations to analyze the above problems in the textbook of elastic mechanics. There are 15 basic partial differential equations
recommend the course of elasticity of Beijing University Edition

6. The dimension of couple itself is the proct of force and distance, so it is not necessary to consider distance in calculation, only force needs to multiply distance. If the concentrated couple makes the beam concave downward, it is a positive value and concave upward is a negative value. However, these positive and negative are relative, as long as each force and couple are unified in an equation. I don't know if you understand. If you still don't understand, just memorize it for the exam. I will understand when I see more later.

7. The bending moment curve of the section with concentrated force turns, and the shear force graph changes abruptly, and the mutation amplitude is equal to the concentrated force value
the bending moment curve at the section of the concentrated couple changes abruptly, the mutation amplitude is equal to the couple value, and the shear force graph does not change.

8. Fra = (3 / 4) QL has the same direction as the graph. The formulas listed in your graph are correct, but the result is wrong. The value of ME1 is - (1 / 2) QL ^ 2, which is substituted into the formula. Don't forget the negative sign. Me2 is a positive sign, so FRB = (1 / 4) QL

9. Because it is set to be positive counterclockwise and negative clockwise; You can also set the counter clockwise to be negative and the clockwise to be positive, which way will not affect the calculation result.

10. Best answer: mainly use the formula FX = fcos α, Fy=Fsin α, Where f is the force, α Is the angle between F and the positive half axis of X. ① F1=30 kN, α= 30º; ② F2=40 ...