Hooke's Theorem-Within the elastic limit of materials, strain is directly proportional to stress.
The deflection curve of beam is approximately a differential equation, and the approximate reason lies in the assumption of small deflection deformation, so y'≈0 is approximately considered in the curvature expression of deformation, thus simplifying the formula and obtaining the approximate differential equation of deflection curve of beam. This is the root cause of approximation. In fact, it does differ from the facts in the case of large deflection, but it is accurate enough in the case of small deflection. In practical application, a large number of small deflection deformation problems are involved, so the differential equation of deflection curve can also be used to obtain the solution that meets the accuracy requirements. But if it is extended to large deformation, it will lead to obvious errors, so we must be careful.
Similarities and differences between ordinary beam deflection equation and compression bar buckling deflection equation The most essential difference is that ordinary beam deflection equation does not consider the influence of axial force, while compression bar buckling deflection equation considers the influence of axial force. As for small deformation and large deformation, this is not the most essential difference, because ordinary beam deflection curve equation can also describe large deformation, but there is no analytical solution after considering large deformation.
The reasons are as follows: the deflection curve equation of ordinary beam studies the situation far from instability, and its influence can be ignored when the axial force is small; The buckling deflection equation of compression bar studies the situation before and after buckling. At this time, the axial force is too large to be ignored, and its influence cannot be ignored. In fact, Timoshenko has studied the beam deflection curve equation considering axial force. This equation can be simplified to the ordinary beam deflection curve equation, and can also accurately predict the spiritual load of beam instability. It is a nonlinear equation with partial linear relationship. You can read his book if you are interested.
What is the deflection equation of cantilever beam? (1) The cantilever beam acts a concentrated load at the rod end (the rod bends downward);
y=-Px^2(3l-x)/(6EI)
P concentrated load
L-bar length
modulus of elasticity
moment of inertia
(2) The cantilever beam exerts concentrated load on the rod (the rod bends downward):
0≤x≤y=-px^2(3a-x)/(6ei)
a≤x≤l y=-Pa^2(3x-a)/(6EI)
A—— Distance from concentrated load to fixed end
(3) The cantilever beam is used as a concentrated couple at the rod end (the rod bends downward):
y=-mx^2/(2EI)
M pair
(4) The cantilever beam acts on the rod with a concentrated couple (the rod bends downward):
0≤x≤y=-mx^2/(2ei)
a≤x≤l y=-ma(x-a/2)/(EI)
(5) The uniform load acts on the cantilever beam (the bar bends downward):
y=-qx(x^2+6l^2-4lx)/(24EI)
Q- uniformly distributed load
What language is tradeblazer's programming based on? Similarities between C# and JAVA: Because both C# and JAVA are developed based on C++, there are many similarities between them, as follows: 1, compilation results of C# and JAVA languages are independent of computers and programming languages, and executable files can be executed in a managed execution environment;
The deflection equation of a cantilever beam is its maximum deflection. A.b.c.d My idea is this: First draw the bending moment under the action of F, and then draw the bending moment diagram under the action of unit force at the same position, and then calculate it in sections by graph multiplication or integral method. Because the only item that affects it in the formula is EI, it can be directly divided according to different stiffness.
What theory is the pricing equation of futures and options based on? Futures pricing equation: the pricing mechanism of futures prices depends on the similarity with spot commodity prices, and there is a certain premium. You can refer to the futures price contract last month. It also refers to foreign variety contracts.
Option pricing formula:
Option pricing theory, that is, option pricing model. Option price refers to a certain fee paid by the contract buyer to the seller when buying and selling options. The buyer obtains the right by paying the option fee, and the seller bears the risk and responsibility by collecting the option fee. The price of options consists of intrinsic price and time price. The intrinsic price of the option is the value of the option itself, that is, the difference between the agreed price of the option and the spot price or market price of the financial instrument. Option pricing theory quantitatively solves the problem of how to price options.
What approximation is the ewald ball based on? The most important application of reciprocal lattice of illustrative diffraction principle is to illustrate and expound the diffraction principle with ewald sphere. According to the first-order Bragg formula 2d sinθ= λ, sinθ=( 1/d)/(2/λ), that is, 1/d and 2/λ which are sinusoidal with θ are 1 respectively.
What equation is the working principle of U-type differential pressure gauge based on? The function of U-shaped differential pressure gauge is to measure the pressure difference between two water sections of pipeline, and the calculation formula is different under different placement forms. In order to change the water column height of the U-shaped differential pressure gauge, it is necessary to change the pressure difference between the two water-passing sections, and the flow velocity can be changed according to Bernoulli equation. Similarly, the measured pipe section can also be changed.
What is the management method of snipe ec based on?
(1) The theory of human nature hypothesis was put forward by western management scientists, and its contents include economic man hypothesis, social man hypothesis, self-fulfilling man hypothesis and complex man hypothesis. It has its scientific components, but it also has its one-sidedness. China has its own national characteristics and cultural traditions. Therefore, we can't copy western things, but should analyze and study these theories according to the reality of our country, and get rid of their uselessness.
(2) Marxist analysis of human nature is the guiding ideology of our study of human nature. Marx pointed out: "the essence of man is not an abstract thing inherent in a single person." In reality, it is the sum of all social relations. " Therefore, we can't study human nature without the influence of society and organization, but we should object to saying that human nature is innate and unchangeable. It can be seen that the assumptions of economic man, social man and self-fulfilling man all have their one-sidedness and limitations, while the assumptions of complex man are dialectical and reasonable.