Calculation formula of M-chain force
The calculation formula of the maximum deflection of simply supported beam under various loads:
the maximum deflection under uniform load is in the middle of the beam, and the calculation formula is: ymax = 5ql ^ 4 / (384ei)
where ymax is the maximum deflection in the middle of the beam span (mm)
q is the standard value of average wiring load (KN / M)
e is the elastic molus of steel. For structural steel, e = 2100000 n / mm ^ 2
I is the section moment of inertia of steel, which can be found in the section steel table (mm ^ 4)
the maximum deflection under a concentrated load in the middle of the span is in the middle of the beam, and its calculation formula is: ymax = 8pl ^ 3 / (384ei) = 1pl ^ 3 / (48ei)
where ymax is the maximum deflection in the middle of the beam span (mm)
P is the sum of the standard values of each concentrated load (KN)
e is the elastic molus of steel. For structural steel, e = 2100000 n / mm ^ 2
I is the section moment of inertia of steel, which can be found in the section steel table (mm ^ 4)
the maximum deflection under two equal concentrated loads with equal spacing between spans is in the middle of the beam span, and the calculation formula is: ymax = 6.81pl ^ 3 / (384ei)
where ymax is the maximum deflection in the middle of the beam span (mm)
P is the sum of the standard values of each concentrated load (KN)
e is the elastic molus of steel. For structural steel, e = 2100000 n / mm ^ 2
I is the section moment of inertia of steel, which can be found in the section steel table (mm ^ 4)
the maximum deflection under three equal concentrated loads with equal spacing between spans is calculated as follows: ymax = 6.33pl ^ 3 / (384ei)
where ymax is the maximum deflection in the middle of the beam span (mm)
P is the sum of the standard values of each concentrated load (KN)
e is the elastic molus of steel. For structural steel, e = 2100000 n / mm ^ 2
I is the section moment of inertia of steel, which can be found in the section steel table (mm ^ 4)
when the cantilever beam is subjected to uniform load or concentrated load at the free end, the maximum deflection at the free end is respectively, and the calculation formula is:
ymax = 1ql ^ 4 / (8ei), ymax = 1pl ^ 3 / (3ei)
q is the standard value of the average wiring load (KN / M), and P is the sum of the standard values of each concentrated load (KN)
< H2 > extended data:deflection is the linear displacement of the member axis in the direction perpendicular to the axis or the plate and shell middle plane in the direction perpendicular to the middle plane when the force or non-uniform temperature changes
the deflection of slender body (such as beam or column) refers to the displacement of each point on its axis in the normal plane of the axis at that point
the deflection of thin plate or shell refers to the displacement of each point on the midplane normal at this point. The rule that the deflection of each point on the object changes with position and time is called deflection function or displacement function. It is one of the research methods of solid mechanics to calculate strain and stress by solving deflection function
deflection curve when plane bending, the axis of the beam will become a plane curve in the longitudinal symmetry plane of the beam, which is called the deflection curve of the beam
The calculation formula of deflection is as follows: ymax = 5ql ^ 4 / (384ei) (for a simply supported beam of length L, EI is the bending stiffness of the beam under the uniformly distributed load q)the deflection is related to the load size, the section size of the member and the material physical properties of the member
Deflection the linear displacement of the centroid of the cross section along the direction perpendicular to the axis ring bending deformation is called deflection γ Expressionrotation angle the angle at which the cross section turns relative to its original position ring bending deformation is called rotation angle θ Expression
Deflection curve equation the values of deflection and rotation angle vary with the position of the section. When discussing the problem of bending deformation, we usually choose the coordinate axis X to be positive to the right and the coordinate axis y to be positive to the down. After the coordinate axis is selected, the deflection of each cross section of the beam is calculated γ It will be a function of the position coordinate X of the cross section, and its expression is called the deflection curve equation of the beam, i.e γ= f(x) Obviously, the value of the deflection curve equation at section x is equal to the deflection at that section Construction Engineering)slope of deflection curve at section position coordinate X, or deflection γ The first derivative of X is equal to the angle of the section
regulations on the positive and negative signs of deflection and rotation angle: in the coordinate system selected in the figure above, the upward deflection is positive, and the rotation angle of counterclockwise turning is positive
reference link: Network - deflection
Formula: (G-C)% = (tm-69.3) × Under certain conditions (pH7.0, 0.165mnacl), TM value was proportional to (GC)%. Therefore, the percentage of bases in DNA can be calculated by measuring TM value
under certain conditions, the level of TM was determined by the content of G-C in DNA molecule. When G-C content is high, TM value is relatively high, otherwise it is low. This is because there are more hydrogen bonds between G-C than A-T, and more energy is needed to break the chain
extended data
DNA in natural state will undergo denaturation at relatively high temperature (70-90 ℃). At this time, the double helix will unravel into a single strand and become an irregular coil. On the other hand, there is a "hyperchromic effect" in optical properties, that is, the value of ultraviolet absorption (at the wavelength of 260 nm) increases. This is similar to the melting phenomenon of ordinary crystals
the temperature range of DNA "melting" is narrow, only a few degrees. Generally, the temperature when the hyperchromic effect reaches half of the maximum value is called the melting temperature (or melting point) of DNA, which is expressed by the symbol TM. Different DNA sequences have different TM values. The higher the G-C content in DNA, the higher the TM value
1. Dimension chain in the process of machine assembly or parts processing, a closed dimension group formed by interconnected dimensions is called dimension chain. The gap A0 is connected with other dimensions to form a closed dimension group to form a dimension chain
2. Ring - every dimension listed in the dimension chain is called a ring, A0, A1, A2, A3... Are rings. The length ring is represented by capital italics Latin letters a, B, C, etc; The angle ring is in small Greek italics α，β And so on
3. Closed ring is a ring naturally formed in the dimension chain after assembly or processing, which is called closed ring. The lower corner of the closed ring is indicated by "0"
4. Constituent ring all the rings in the dimension chain that have influence on the closed ring are called constituent rings. The lower corner of the ring is represented by Arabic numerals
5. Increasing ring is a kind of constituent ring in the dimension chain. The change of the constituent ring causes the change of the closed ring in the same direction, and the constituent ring is increasing ring. As shown in A3
6. Subtractive ring is a kind of constituent ring in the dimension chain. Because the change of the constituent ring causes the reverse change of the closed ring, this kind of constituent ring is subtractive ring
7. Compensation ring - a pre selected group of rings in the dimension chain can be changed in size or position to make the closed ring meet the specified requirements, and the component ring is compensation ring< In mechanical manufacturing, the dimension tolerance is usually expressed by basic dimension (a), upper deviation (ES) and lower deviation (EI), and can also be expressed by maximum limit dimension (Amax), minimum limit dimension (Amin), basic dimension (a) and intermediate deviation Δ) And tolerance δ) The relationship between them is shown in the figure
(1) the basic dimension Ao of the closed ring is equal to the sum of the basic dimensions (AP) of all the increasing rings minus the sum of the basic dimensions (AQ) of all the decreasing rings, i.e.
where m is the number of constituent rings; K - the number of increasing rings< br /> ξ I-the size transfer coefficient of the i-th component ring. For the linear size chain, the increasing ring is the most important ξ I = 1, the number of decreasing rings ξ i＝－1
(2) the limit dimension of the ring Amax = a + es Amin = a-ei
(3) the limit deviation of the ring ES = amax-a EI = a-amin
(4) the intermediate deviation of the closed ring
where: Δ I-the intermediate deviation of the i-th constituent ring
conclusion: the mean deviation of the closed loop is equal to the sum of the mean deviations of all the increasing loops minus the sum of the mean deviations of all the decreasing loops< (5) tolerance of closed loop
conclusion: tolerance of closed loop is equal to the sum of tolerance of all components< (6) the intermediate deviation of the constituent ring
Δ I = (ESI + EII) / 2
(7) limit size of closed loop
conclusion: the maximum value of closed loop is equal to the sum of the maximum value of all increasing loops minus the sum of the minimum value of all decreasing loops
conclusion: the minimum value of a closed ring is equal to the sum of the minimum values of all increasing rings minus the sum of the maximum values of all decreasing rings
(8) limit deviation of closed cycle
conclusion: the upper deviation of closed cycle is equal to the sum of the upper deviations of all increasing cycles minus the sum of the lower deviations of all decreasing cycles
conclusion: the lower deviation of closed rings is equal to the sum of the lower deviations of all increasing rings minus the sum of the upper deviations of all decreasing rings.
"Linear velocity" is the velocity of any point of an object moving in a circle around a fixed axis. Its general definition is the instantaneous velocity of a particle (or points on an object) in curvilinear motion (including circular motion)
The calculation formula is: v = s / △ T, also v = 2 π r/T In the uniform circular motion, the linear velocity is equal to the arc length (s) and the time (△ T) of the moving particle. In uniform circular motion, although the magnitude of linear velocity does not change, its direction changes all the time The direction of the linear velocity is along the tangent direction of the moving track, so it is also called tangential velocity. It is a physical quantity describing the speed and direction of a particle moving in a curve. The instantaneous velocity of each point on an object moving in a curve, its direction is along the tangent direction of the moving orbit
the speed of circular motion can be measured by the ratio of the arc length passed by the object to the time spent. If the object moves from m to N, t passes through point a at some time. In order to describe the speed of motion near point a, we can take a very short period of time △ t from now on. During this period of time, the object moves from a to B, and the arc length is △ L. The ratio △ L / △ t reflects the speed of an object's motion, which is called linear velocity. It is expressed by V, that is, v = △ L / △ t
The linear velocity can be divided into average value and instantaneous value. If the time interval is very small, the instantaneous linear velocity is obtainedlinear velocity is a vector, which has size and direction. The direction of linear velocity of an object moving in a circle changes all the time and always points to the tangent direction of the point
the time change rate of angular displacement of object motion is called instantaneous angular velocity (also known as instantaneous angular velocity), the unit is radian / second (rad / s), and the direction is determined by the right-hand screw rule
angular velocity in uniform circular motion: for uniform circular motion, angular velocity ω It is a constant, which can be used to calculate the angular displacement of a moving object along the line connecting the center of a circle Δθ And the corresponding time Δ The ratio of T ω= △ θ/ Δ t can also be calculated by V (linear velocity) / R (radius)
It can be seen that the velocity of a particle in a rigid body can be decomposed into two terms: the velocity of a fixed reference point in the rigid body plus an outer proct containing the angular velocity of the particle relative to the reference point. Compared with O & # 39; The angular velocity of a point to o, which is & quot; Spin & quot; Angular velocity It is very important that each particle in the rigid body has the same spin angular velocity, which is independent of the origin of the rigid body or the laboratory coordinate system. In other words, this is the real physical quantity of a rigid body, which has nothing to do with the choice of coordinate system. However, the angular velocity of the reference point on the rigid body relative to the origin of the laboratory coordinate system is related to the choice of the coordinate system. For convenience, the center of mass of the rigid body is usually chosen as the origin of the rigid body coordinate system, which greatly simplifies the mathematical expression of the angular momentum of the rigid body < H2 > reference link: network linear speedlet's take an example:
suppose there are jd1 and JD2, and the chain breaking K1 + 100 = K1 + 105 is on the front straight line segment of JD2, It is a 5m short chain
then, when the chain is broken from the broken point, jd1 is not only calculated to Hz point, but to K1 + 100 point
JD2 is not calculated from zh point, but from K1 + 105 point
that is to say, the station number in the middle of K1 + 100 ~ K1 + 105 is blank, so there is no need to calculate
suppose that there are jd3 and jd4, broken chain K1 + 100 = K1 + 996 on the front straight line of jd4, It is a 4m long chain
then, when the chain is disconnected from the broken point, jd3 is not calculated to Hz point, but to K1 + 100 point.
JD2 is not only calculated from zh point, but from K1 + 996 point.
that is to say, the stations between K1 + 996 and K1 + 100 are calculated twice in jd3 and jd4 respectively, and the results of the two times are absolutely different. It is necessary to distinguish the repeated stations, Which is before the chain breaking point and which is after the chain breaking point
solution: if the mass of an object is known, the formula g = Mg can be used to calculate gravity,
where G is the gravity of the object, and its unit is Newton,
m is the mass of the object, Its unit is kilogram,
G = 9.8n/kg, read as 9.8n/kg, which means: the gravity of an object with a mass of 1kg is 9.8N.
so the answer is: the weight of the object; Quality; 9.8N/kg The gravity of an object with a mass of 1kg is 9.8N.
comments: This paper studies the relationship between gravity and mass and the physical meaning of G, which belongs to the basic question type.
analysis: understand the meaning of each quantity in the gravity formula, and know the size and physical meaning of G.
solution: the relationship between gravity and mass: g = mg, Where g stands for the gravity of the object, m stands for the mass of the object, g = 9.8n/kg, read as 9.8n/kg, it means that the gravity of the object with a mass of 1kg is 9.8N.
so the answer is: g = mg, gravity, mass, 9.8n/kg, 9.8n/kg, the gravity of the object with a mass of 1kg is 9.8N.
comments: this question tests students' understanding of the gravity formula, Especially for the understanding of G
analysis: the relationship between gravity and mass is: the gravity of an object is directly proportional to its mass, the formula is: g = mg, and then use the memory analysis of the formula g = mg.
solution: if the mass of an object is known, the formula g = Mg can be used to calculate the gravity,
where G is the gravity of the object, and its unit is Newton, M is the mass of the object, Its unit is kilogram.
the physical meaning of the formula is that the gravity of an object is directly proportional to its mass.
so the answer is: g = mg, gravity, Newton, mass, kilogram. The gravity of an object is directly proportional to its mass.
comments: This paper examines the calculation formula of gravity, The key point is students' understanding and application of the formula g = mg
the correct writing of G = mg is g = mg, where G is gravity, G is acceleration of gravity, and M is mass. Gravity refers to the force exerted on an object e to the attraction of the earth. The calculation formula is g = mg. G is a proportional coefficient, also known as gravitational acceleration, with a value of 9.8n/kg.
Divide the mass by the volume to get the transmitted weight, that is, the load on the belt drive, the positive pressure n, n times the friction coefficient to get the friction force F, and then use the following formula to approximate (note the approximate calculation) to calculate the transmitted power P, P = F × Velocity v ÷ 1000 In this way, the calculated power is relatively large, which is a rough calculation
According to the different working conditions of gear transmission, it can be divided into closed gear transmission, open gear transmission and semi open gear transmission. In the open gear transmission, the teeth are exposed, and the st is easy to fall on the tooth surface In the closed gear transmission, the gear teeth are enclosed in the box, which can ensure good working conditions and is widely used; The working condition of the semi open gear transmission is better than that of the open gear transmission. The large gear is partially immersed in the pumping pool and has a simple protective cover, but there are still foreign objects
extension data:
when the gear is working, the front meshing is under the repeated action of alternating contact stress, and a number of small cracks will appear on the tooth surface near the pitch line. As the crack propagates, small pieces of metal will peel off
The continuous expansion oftooth surface pitting will affect the stability of transmission, and proce vibration and noise, resulting in the gear can not work normally. Pitting is a common failure form of closed gear transmission with good lubrication. Increasing the hardness of the tooth surface and recing the surface roughness can improve the anti pitting ability of the tooth surface, and open gear transmission can avoid pitting because of the rapid wear of the tooth surface
when the gear teeth are meshing, the relative sliding, especially when the external hard particles enter between the meshing faces, will cause the surface wear of the gear teeth. After the tooth surface is graally worn, the tooth surface will lose the correct tooth shape, which will lead to the tooth being too thin and broken in serious cases. The tooth surface wear is the main failure form of open gear transmission. In order to rece wear, the important gear transmission should adopt closed transmission, and pay attention to lubrication