Article 1 static

Article 1 static

Requirements:

1. It has the initial ability to identify Theoretical Mechanics Problems from simple practical problems and abstract them into Theoretical Mechanics Models.

2. Based on the specific conditions and requirements of the problem, the study objects can be properly selected from the simple object system, and the plot can be correctly drawn.

3. Have a clear understanding of the force and the force couple properties and their effects, and be able to skillfully calculate the projection Force Moment of the force, and use the force system to simplify the theoretical computation of the principal vector and the main moment of the general force system.

4. Use the equilibrium condition correctly to solve the static problem. Must be proficient in solving the Balance Problem of the simple thing System in the plane.

Key points of this Article

1. Concept of force, rigid body, balance, constraint, equivalent, torque, force even moment, sliding friction and extreme sliding friction.

2. Static kilometer, simplified force system, balance condition and equilibrium equation of force system.

3. Force Analysis of objects, projection of forces and torque calculation, and Solution to the balance problem between objects and systems.

Difficulties

1. Constraints and binding force, establishment of equivalent force system ideas, and analysis of the Balance Problem of the thing system.

2. Apply the friction angle and self-locking concept to the balance problem.

 

Chapter 1 Static Analysis

Requirements in this Chapter

1. In-depth understanding, rigid body, balance, constraints, and other important concepts.

2. Static kilometers are the theoretical basis of static data and require in-depth understanding.

3. Clear the characteristics of smooth contact surface constraints, flexible constraints, and smooth hinge constraints.

4. Ability to correctly analyze the force of a single object and its system.

Difficulties in this Chapter

1. Concept of constraints, characteristics of smooth hinge constraints.

2. Stress Analysis of the thing system.

I. Basic Concepts

1.Balance: It refers to the State in which an object moves at a constant speed or in a straight line relative to the ground. Balancing is a special form of mechanical motion.

2.Rigid Body: The size and shape of an object remain unchanged after it is subjected to force. The distance between any two points in the body remains unchanged.

3. mechanical interaction between objects, which changes the motion and shape of objects.

The effect of changing the motion of an object isExternal Effect, Also calledMotion EffectThe effect of changing the shape of an object isInternal Effect, Also calledDeformation Effect

4.Force System: A group of forces acting on objects.

5.Equivalent Force System: If the two force systems have identical effects on objects, the two force systems are called equivalent force systems. As

The two equivalent force systems can be replaced by each other.Equivalent replacement of Force System.

6. Simplified force system: replace a complex force system with a simple force system.

Heli: The effects of a force are the same as those of a force system.

Balance force:

Ii. Static Principle

1. Balance of two forces: The two forces acting on the rigid body to balance the rigid body are: Equal size, opposite direction, and acting on a straight line.
   

This principle can be applied to perform simple stress analysis. Component AB in A, B each by A force and balance, then the force of the two line must be in the AB line, like this by the Force and balance of the component, it is called a two-force component (two-force rod ).

1. Addition, subtraction, and balance Power System: Adding or subtracting any balance force in the known force system acting on the rigid body does not change the effect of the Force System on the rigid body.
   

Inference 1Transfer Ability: The force acting on the rigid body can be moved along its line to any point in the same rigid body, without changing its effect on the rigid body.

Proof:

Conclusion 1: For a rigid body, the starting point is not important. What affects the force line is the force line. Therefore, for a rigid body, the three elements of force are size, direction, and line.

3.Parallelogram law of force: The two forces acting on a certain point of an object can be combined into a force, and the force also acts on this point, the force size and direction can be determined by the diagonal lines of the parallelogram formed by the adjacent edge.

Triangle rule of force:

Inference 2Three-force equilibrium Orthogonal Theorem: When a rigid body is balanced by three forces, if the two force lines intersect at one point, the third force line will pass through the intersection of the two force lines, and the three forces are in the same plane.

Evidence: (graphic)

Rule from Parallelogram

The two forces must be in the same line.

4.Law of force and ReactionThe interaction force between two objects is always equal in size and opposite in direction. They act on two objects along the same line.

5.Rigid Principle: If the deformed body in the balance state is rigid, the balance state remains unchanged. (Example) specific examples should be provided.

This principle indicates that the equilibrium condition of a rigid body is a necessary condition for the equilibrium of the deformed body.

Iii. Constraints and binding force

1. Basic concepts:

Free body: An object that can be freely moved in a space without restrictions. Example!

Non-free body: An object that is limited by a given condition. Example!

Constraints: Restrictions imposed on the motion of objects in advance.

Binding Force: The force on the constrained object. It is a dynamic force.

(Main power: The force that allows an object to move or to a moving trend .)

Three elements of binding force: Binding point: in contact with each other

Direction: opposite to the direction of movement of the object that the constraint can block.

Size: Unknown, determined by the main power.

2. Common constraints

① Flexible constraints:

Concept: a constraint that consists of soft, non-expandable, non-weighted, flexible connection objects such as chains and ropes.

Restricted motion: restrict the movement of an object along the flexible stretch direction.

Binding Force direction: along the rope, it deviates from the object and is a tension.

Other examples:

② Smooth contact surface constraints

Concept: The two objects are directly in contact, regardless of the friction at the contact.

Restricted motion: it limits the movement of an object moving toward the contact surface along the public line of the contact point.

Binding Force direction: it is the pressure that points to the object along the public line of the contact point.

More examples:

③ Smooth hinge Constraint

Movable hinge bearing fixed hinge Bearing

 

Concept: the drill of two components has a circular hole of the same size and is constrained by the smooth pin connection with the same diameter of the circular hole. Restricted motion: the movement of an object along any radial direction of the cylindrical pin is restricted, and the rotation around the cylindrical pin axis and the movement of the horizontal line of the cylindrical pin axis cannot be restricted.

Binding analysis Diagram

Three binding factors:

Vertex: touchpoint, but this vertex cannot be determined beforehand.

Direction: along the direction of the Public line of the contact point, perpendicular to the axis, is the pressure. But in fact, because the contact point cannot be determined in advance, the binding direction cannot be determined in advance. Generally, two orthogonal unknown split forces are used.

Size: determined by the main power.

Direction: cross axis, perpendicular to the axis, without changing the direction, usually expressed by orthogonal force.

④ Roller Bearing

 

Concept: the hinge bearing is supported by several rollers on a smooth bearing. It is a combination of smooth contact surface constraints and smooth hinge constraints.

Restricted motion: The movement along the normal direction of the bearing surface is restricted.

Binding Force:

Binding Force direction: vertical to the bearing surface, pointing to knowledge.

Iv. Force Analysis and plot of Objects

1.Constraint Relief Principle: When the constrained object is in a balance under the action of some main power, if some or all of its constraints are removed and replaced with corresponding binding force, the balance of the object will not be affected.

2. Force Analysis and plot

For example, it is known that the weight of the block is P, the weight of the ball is g, the weight of the pulley is not counted, and the weight of each rod is not counted.

Solution: 1 block is the research object, and Stress Analysis

2 ball as the research object, Stress Analysis

3 kD rod as the research object, Stress Analysis

4 de rod as the research object, Stress Analysis

5 pulley as the research object, Stress Analysis

6 Overall: stress analysis,