Background
Several real-world electromagnetic problems like scattering, radiation, waveguiding etc, are not analytically calculable, for the multitude of irregular geometries designed and used. The inability to derive closed form solutions of Maxwell's equations under various constitutive relations of media, and boundary conditions, is overcome by computational numerical techniques. This makes computational electromagnetics(CEM), an important field in the design, and modeling of antenna, radar, satellite and other such communication systems, nanophotonic devices and high speed silicon electronics, medical imaging, cell-phone antenna design, among other applications.
CEM problems typically solve for the problem of computing the E (Electric), and H (Magnetic) fields across the domain of the problem (i.e to calculate antenna radiation pattern, for an arbitrarily shaped antenna structure is solved by CEM). Also, power flow direction (poynting vector), normal modes of a waveguide, dispersion of wave due to media, and scattering are quantities of interest, that can be computed from the knowledge of the E and H fields. CEM models, assume symmetry, simplify real world structures to cylinders, spheres, and other regular geometrical objects. CEM models, extensively make use of symmetry, and solve for reduced dimensions of the system from 3 spatial dimensions, to 2D and even 1D. CEM can be formulated into a various problems depending on any of the several quantities of interest mentioned previously. An Eigen value problem formulation of CEM allows us to calculate steady state normal modes in a structure. Transient response and impulse field effects are more accurately modeled by CEM in time domain, by FDTD. Treating curved geometrical objects is done more accurately by using finite elements FEM, or non-orthogonal grids. Beam propagation methods like BPM, solve for the power flow in waveguides. So, CEM model used is application specific, even if different techniques converge to the same field and power distributions in the modeled domain.
[edit] Methods
CEM can be used to model the domain generally by discretizing the space in terms of grids (both orthogonal, and non-orthogonal), and then solve the Maxwell's equations at each point in the grid. Naturally, such discretization of the computational space consumes computer memory, and solving the equations takes a longer time. Large scale CEM problems place computational limitations in terms of memory space, and CPU time on the computer. Generally CEM problems, as of 2007, are run on supercomputers, high performance clusters, vector processors and parallel computers; see article on, parallel computing for more computer/machine specific details. Typical formulations involve either time-stepping through the Maxwell's equations over whole domain for each time instant; or through banded matrix inversion to calculate the weights of basis functions, when modeled by Finite element methods; or matrix products when using transfer matrix methods; or calculating integrals when
using method of moments (MoM); or using FFT, and time iterations when calculating by the split-step method or by BPM.
[edit] Choice of methods
Discussion of which method is chosen when should go here. Integral equation solvers versus differential equation solvers. When and why to use high-frequency approximations.
[edit] Maxwell's equations in hyperbolic PDE form
Maxwell's equations can be formulated as a hyperbolic system of partial differential equations. This gives access to powerful mathematical theories for the numerical solutions of hyperbolic PDE's.
It is assumed that the waves propagate in the (x,y)-plane and restrict the direction of the magnetic field to be parallel to the z-axis and thus the electric field to be parallel to the (x,y) plane. The wave is called a transverse electric (TE) wave. In 2D and no polarization terms present, Maxwell's equations can then be formulated as
where u, A, B, and C are defined as
[edit] Integral equation solvers
[edit] The discrete dipole approximation
The discrete dipole approximation is a flexible technique for computing scattering and absorption by targets of arbitrary geometry. The formulation is based on integral form of Maxwell equations. The DDA is an approximation of the continuum target by a finite array of polarizable points. The points acquire dipole moments in response to the local electric field. The dipoles of course interact with one another via their electric fields, so the DDA is also sometimes referred to as the coupled dipole approximation. Resulting linear system of equations is commonly solved using the conjugate gradient iterations. Because discretization matrix has symmetries (the integral form of Maxwell equations has form of convolution) it is possible to use Fast Fourier Transform to multiply matrix times vector during the conjugate gradient
iterations.
[edit] Method of moments (MOM) or boundary element method (BEM)
The method of moments (MOM)or boundary element method(BEM)is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form). It can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, fracture mechanics, and plasticity.
It has become more and more popular since the 1980s. Because it requires calculating only boundary values, rather than values throughout the space defined by a partial differential equation, it is significantly more efficient in terms of computational resources for problems where there is a small surface/volume ratio. Conceptually, it works by constructing a "mesh" over the modeled surface. However, for many problems boundary element methods are significantly less efficient than volume-discretization methods (finite element method, finite difference method, finite volume method). Boundary element formulations typically give rise to fully populated matrices. This means that the storage requirements and computational time will tend to grow according to the square of the problem size. By contrast, finite element matrices are typically banded (elements are only locally connected) and the storage requirements for the system matrices typically grow quite linearly with the problem size. Compression techniques (e.g. multipole expansions or adaptive cross approximation/hierarchical matrices) can be used to ameliorate these problems, though at the cost of added complexity and with a success-rate that depends heavily on the nature of the problem being solved and the geometry involved.
BEM is applicable to problems for which Green's functions can be calculated. These usually involve fields in linear homogeneous media. This places considerable restrictions on the range and generality of problems to which boundary elements can usefully be applied. Nonlinearities can be included in the formulation, although they will generally introduce volume integrals which then require the volume to be discretized before solution can be attempted, removing one of the most often cited advantages of BEM.
[edit] Fast multipole method (FMM)
The fast multipole method (FMM) is a computational electromagnetic technique that may be applied instead of techniques like the method of moments (MoM) or Ewald summation. It is an accurate simulation technique and is computationally more efficient than the MoM. Both memory and processor runtime requirements are greatly reduced over the MoM. The FMM was first introduced by Greengard and Rokhlin and is based on the multipole expansion technique. Can be used to accelerate MOM.
[edit] Partial Element Equivalent Circuit method (PEEC)
The Partial Element Equivalent Circuit (PEEC) is a 3D full-wave modeling method suitable for combined electromagnetic and circuit analysis. Unlike the method of moments(MoM), PEEC is a full spectrum method valid from dc to the maximum frequency determined by the meshing. In the PEEC method, the integral equation is interpreted as Kirchhoff's voltage law applied to a basic PEEC cell which results in a complete circuit solution for 3D geometries. The equivalent circuit formulation allows for additional SPICE type circuit elements to be easily included. Further, the models and the analysis apply to both the time and the frequency domain. The circuit equations resulting from the PEEC model are easily constructed using a modified loop analysis (MLA) or modified nodal analysis (MNA) formulation. Besides providing a dc solution, it has several other advantages over a MoM analysis for this class of problems since any type of circuit element can be included in a straightforward way with appropriate matrix stamps. The PEEC method has recently been extended to include nonorthogonal geometries. This model extension, which is consistent with the classical orthogonal formulation, includes the Manhattan representation of the geometries in addition to the more general quadrilateral and hexahedral elements. This helps in keeping the number of unknowns at a minimum and thus reduces computational time for nonorthogonal geometries. [1]
[edit] Differential equation solvers
[edit] Finite-difference time-domain (FDTD)
Finite-difference time-domain (FDTD) is a popular computational electrodynamics modeling technique. It is considered easy to understand and easy to implement in software. Since it is a time-domain method, solutions can cover a wide frequency range with a single simulation run.
The FDTD method belongs in the general class of grid-based differential time-domain numerical modeling methods. Maxwell's equations(in partial differential form) are modified to central-difference equations, discretized, and implemented in software. The equations are solved in a leapfrog manner: the electric field is solved at a given instant in time, then the magnetic field is solved at the next instant in time, and the process is repeated over and over again.
The basic FDTD algorithm traces back to a seminal 1966 paper by Kane Yee in IEEE Transactions on Antennas and Propagation. The descriptor "Finite-difference time-domain" and its corresponding "FDTD" acronym were originated by Allen Taflove in a 1980 paper in IEEE Transactions on Electromagnetic Compatibility. Since about 1990, FDTD techniques have emerged as primary means to model many scientific and engineering problems dealing with electromagnetic wave interactions with material structures. Current FDTD modeling applications range from near-DC
(ultralow-frequency geophysics involving the entire Earth-ionosphere waveguide) through microwaves (radar signature technology, antennas, wireless communications devices, digital interconnects, biomedical imaging/treatment) to visible light (photonic crystals, nanoplasmonics, solitons, and biophotonics). Approximately 30 commercial and university-developed FDTD software suites are available for use (see below).
[edit] Multiresolution time-domain (MRTD)
An adaptive alternative to the finite difference time domain method (FDTD) based on wavelet analysis.
[edit] Finite element method (FEM)
The finite element method(FEM)is used for finding approximate solution of partial differential equations(PDE) and integral equations. The solution approach is based either on eliminating the differential equation completely (steady state problems), or rendering the PDE into an equivalent ordinary differential equation, which is then solved using standard techniques such as finite differences, etc.
In solving partial differential equations, the primary challenge is to create an equation which approximates the equation to be studied, but which is numerically stable, meaning that errors in the input data and intermediate calculations do not accumulate and cause the resulting output to be meaningless. There are many ways of doing this, all with advantages and disadvantages. The Finite Element Method is a good choice for solving partial differential equations over complex domains or when the desired precision varies over the entire domain.
[edit] Finite integration technique (FIT)
The finite integration technique(FIT)is a spatial discretization scheme to solve electromagnetic field problems in time and frequency domain numerically. It preserves basic topological properties of the continuous equations such as conservation of charge and energy. FIT was proposed in 1977 by Thomas Weiland and has been enhanced continually over the years [2]. This method covers the full range of electromagnetics, from static up to high frequency and optic applications and is the basis for the commercial simulation tool CST Studio Suite ? developed by Computer Simulation Technology (CST AG).
The basic idea of this approach is to apply the Maxwell’s equations in integral form to a set of staggered grids. This method stands out due to high flexibility in geometric modeling and boundary handling as well as incorporation of arbitrary material distributions and material properties such as anisotropy, non-linearity and dispersion. Furthermore, the use of a consistent dual orthogonal grid (e.g.
Cartesian grid) in conjunction with an explicit time integration scheme (e.g. leap-frog-scheme) leads to extremely high efficient algorithms referred to both computation time and memory requirements which are especially adapted for transient field analysis in RF applications.
[edit] Pseudospectral time domain (PSTD)
This class of marching-in-time computational techniques for Maxwell's equations uses either discrete Fourier or Chebyshev transforms to calculate the spatial derivatives of the electric and magnetic field vector components that are arranged in either a 2-D grid or 3-D lattice of unit cells. PSTD causes negligible numerical phase velocity anisotropy errors relative to FDTD, and therefore allows problems of much greater electrical size to be modeled. For a recent comprehensive summary of PSTD techniques for Maxwell's equations, see Q. Liu and G. Zhao[3].
[edit] Pseudo-spectral spatial domain (PSSD)
This approach solves Maxwell's equations by propagating them forward in a chosen spatial direction. The fields are therefore held as a function of time, and (possibly) any transverse spatial dimensions. The method is pseudo spectral because temporal derivatives are calculated in the frequency domain with the aid of fast Fourier transforms. Because the fields are held as functions of time, this enables arbitrary dispersion in the propagation medium to be rapidly and accurately modelled with minimal effort. See J.C.A. Tyrrell et al.[4].
[edit] Transmission line matrix (TLM)
Transmission line matrix (TLM) can be formulated in several means as a direct set of lumped elements solvable directly by a circuit solver (ala SPICE, HSPICE, et al.), as a custom network of elements or via a scattering matrix approach. TLM is a very flexible analysis strategy akin to FDTD in capabilities, though more codes tend to be available with FDTD engines.
[edit] Other methods
[edit] Physical optics (PO)
Physical optics(PO)is the name of a [[high frequency approximation (short-wavelength approximation) commonly used in optics, electrical engineering and applied physics. It is an intermediate method between geometric optics, which ignores wave effects, and full wave electromagnetism, which is a precise theory.
The word "physical" means that it is more physical than geometric or ray optics and not that it is an exact physical theory.
The approximation consists of using ray optics to estimate the field on a surface and then integrating that field over the surface to calculate the transmitted or scattered field. This resembles the Born approximation, in that the details of the problem are treated as a perturbation.
[edit] Uniform theory of diffraction (UTD)
The uniform theory of diffraction (UTD) is a high frequency method for solving electromagnetic scattering problems from electrically small discontinuities or discontinuities in more than one dimension at the same point.
The uniform theory of diffraction approximates near field electromagnetic fields as quasi optical and uses ray diffraction to determine diffraction coefficients for each diffracting object-source combination. These coefficients are then used to calculate the field strength and phase for each direction away from the diffracting point. These fields are then added to the incident fields and reflected fields to obtain a total solution.
[edit] Validation
Validation is one of the key issue for most of the electromagnetic simulation codes. The question of the Validation of the simulation codes needs at least a section in this page. With the current development of simulation, it is mandatory for the user to understand and master the validity domain of its simulation. The question is not if the simulation is right or not, the question is to assess: "How far from the reality are the results?".
In order to answer this question, the validation can be made in three different steps:
?Comparison between simulation results and analytical formulation
For example, one can assess the value of the RCS of a plate with the analytical formula:
where A is the surface of the plate and λ the wavelength. The next curve presenting the RCS of a plate computed at 35 GHz can be used as reference example.
?Cross-comparison between codes
For example the cross comparison in the validity domain of results from method of moments and asymptotic methods in their validity domains. As an illustration, the company OKTAL-SE made common development and cross comparison with the french research institute ONERA, comparing Method of Moment and Asymptotic methods.
The cross comparison helps the validation process of the SE-RAY-EM code of
OKTAL-SE. Illustration of the comparison between the SE-RAY-EM code and the ONERA reference code (right image).
Comparison of simulation results with measurement
The final validation step is made by comparison between measurements and simulation. A very impressive example is given by the RCS calculation by SE-RAY-EM and the measurement made by FGAN-FHR of a complex metallic object at 35GHz. The computation implements GO, PO and PTD for the edges.
The full article presents a very interesting match between simulation and measurement (right image). This measurement and simulation have been made in Germany, hosted by the FGAN-FHR. The 3D object is public and not restricted. The measurement setup is presented and some of the differences can be explained by the differences between the experimental setup and its reproduction in the simulation environment.
[edit] References
1^Partial Element Equivalent Circuit (PEEC) homepage
2^T. Weiland, A Discretization Method for the Solution of Maxwell's Equations for Six-Component Fields, Electronics and Communications AEUE, vol. 31, no. 3, pp. 116-120, 1977.
3^Q. Liu and G. Zhao "Advances in PSTD Techniques," Chapter 17 in Computational Electrodynamics: The Finite-Difference Time-Domain Method, A.
Taflove and S. C. Hagness, eds., Boston: Artech House, 2005.
4^ J.C.A. Tyrrell et al J.Mod.Opt. 52, 973 (2005).
双代号网络图计算方法是每年建造师考试中的必考题，小到选择题、大到案例分析题，笔者在此总结2种计算方法，并附实例，供大家参考学习，互相交流，考出好成绩。 双代号网络图计算方法一 一、要点： 任何一个工作总时差≥自由时差 自由时差等于各时间间隔的最小值（这点对六时参数的计算非常用用） 关键线路上相邻工作的时间间隔为零，且自由时差=总时差 最迟开始时间—最早开始时间（最小） 关键工作：总时差最小的工作 最迟完成时间—最早完成时间（最小） 在网络计划中，计算工期是根据终点节点的最早完成时间的最大值 二、双代号网络图六时参数我总结的计算步骤（比书上简单得多） ①② t过程 做题次序： 1 4 5 ES LS TF 2 3 6 FS LF FF
步骤一： 1、A 上再做A 下 2 3、起点的A 上=0，下一个的A 上 A 上 4、A 下=A 上+t 过程（时间） 步骤二： 1、 B 下再做B 上 2、 做的方向从结束点往开始点 3、 结束点B 下=T （需要的总时间=结束工作节点中最大的A 下） 结束点B 上=T-t 过程（时间） 4、B 下=前一个的B 上（这里的前一个是从终点起算的） 遇到多指出去的时，取数值小的B 上 B 上=B 下—t 过程（时间） 步骤三： 总时差=B 上—A 上=B 下—A 下 如果不相等，你就是算错了 步骤四： 自由时差=紧后工作A 上（取最小的）—本工作A 下 =紧后工作的最早开始时间—本工作的最迟开始时间 （有多个紧后工作的取最小值） 例：
双代号网络图计算方法二 一、双代号网络图6个时间参数的计算方法（图上计算法） 从左向右累加，多个紧前取大，计算最早开始结束； 从右到左累减，多个紧后取小，计算最迟结束开始。 紧后左上-自己右下=自由时差。 上方之差或下方之差是总时差。 计算某工作总时差的简单方法：①找出关键线路，计算总工期； ②找出经过该工作的所有线路，求出最长的时间 ③该工作总时差=总工期-② 二、双代号时标网络图 双代号时标网络计划是以时间坐标为尺度编制的网络计划，以实
6 . 基础设计 F+G p max min 6.1.1柱下独立基础计算： 用正常使用极限状态下荷载效应的标准组合中最不利荷载组合来确定基础底面尺寸。用承载能力极限状态下荷载效应的基本组合中最不利荷载组合来进行独立基础的设计计算。 设计资料： 持力层的地基承载力特征值：200ak f KPa = 基础及其台阶上土的平均重度：3/20m KN G =γ 垫层采用10C 混凝土，厚度为mm 100。独立基础采用25C 混凝土，2/27.1mm N f t =，钢筋采用235HPB ，2/210mm N f y =。 柱子尺寸：600×600 计算④轴横向框架地梁传给基础顶面荷载： 1、地梁传给A 、D 轴位置基础顶面荷载： 纵向地梁传来荷载 ① 地梁自重： 25×××= ② 地梁上部材料传来荷载： 墙重： 19×××= 窗重： ××= 横向地梁传来荷载 ① 地梁自重： 25××××= KN 地梁传给A 、D 轴位置基础顶面荷载： ∑F=+++= 2、地梁传给B 、C 轴位置基础顶面荷载： 纵向地梁传来荷载 地梁自重： 25×××= ② 地梁上部材料传来荷载：
墙重： 19××（）×= 门重： ××= 横向地梁传来荷载 ① 地梁自重： 25×××（+）/2= KN 地梁传给B 、C 轴位置基础顶面荷载： ∑F=+++= ⑴ A 、D 轴柱下独立基础设计： 按构造一般要求拟定独立基础的截面尺寸，如下图所示： N= M= V= 1、按轴心荷载初步确定基础底面面积： 20963.5563.77 5.0626020 2.85 ak G N F A m f d γ++≥ ==--? 考虑偏心荷载的影响，将0A 增大%30后有： 201.3 1.3 5.06 6.58A A m ==?= 采用方形基础: 2.6b A m == 6.1.2 计算基底最大压力max p 基础及回填土重：220 2.6 2.85385.32G G Ad KN γ==??= 基底处竖向力合力：963.55385.321384.87k F KN =+=∑ 基底处总力矩：53.0934.620.983.71k M KN m =+?=?∑ 偏心矩 83.71 2.6 0.060.431384.8766 k k M b e m m F = = =<==∑∑ 所以偏心力作用点在基础截面内。 基底最大压力：
统计公差分析方法概述(2012-10-23 19:45:32) 分类：公差设计统计六标准差 统计公差分析方法概述 一.引言 公差设计问题可以分为两类：一类是公差分析(Tolerance Analysis ,又称正计算) ,即已知组成环的尺寸和公差,确定装配后需要保证的封闭环公差；另一类是公差分配(Tolerance Allocation ,又称反计算) ,即已知装配尺寸和公差,求解组成环的经济合理公差。 公差分析的方法有极值法和统计公差方法两类,根据分布特性进行封闭环和组成环公差的分析方法称为统计公差法.本文主要探讨统计公差法在单轴向(One Dimension)尺寸堆叠中的应用。 二.Worst Case Analysis 极值法(Worst Case ,WC)，也叫最差分析法，即合成后的公差范围会包括到每个零件的最极端尺寸,无论每个零件的尺寸在其公差范围内如何变化,都会100% 落入合成后的公差范围内。 <例>Vector loop：E=A+B+C,根据worst case analysis可得 D（Max.）=(20+0.3)+(15+0.25)+(10+0.15)=45.7,出现在A、B、C偏上限之状况 D（Min.）=(20-0.3)+(15-0.25)+(10-0.2)=44.3,出现在A,B、C偏下限之状况 45±0.7适合拿来作设计吗? Worst Case Analysis缺陷： ?设计Gap往往要留很大,根本没有足够的设计空间,同时也可能造成组装困难； ?公差分配时,使组成环公差减小,零件加工精度要求提高,制造成本增加。
以上例Part A +Part B+ Part C，假设A、B、C三个部材,相对于公差规格都有3σ的制程能力水平，则每个部材的不良机率为1-0.9973=0.0027；在组装完毕后所有零件都有缺陷的机率为：0.0027^3=0.000000019683。这表明几个或者多个零件在装配时,同一部件的各组成环,恰好都是接近极限尺寸的情况非常罕见。 三.统计公差分析法 ?由制造观点来看,零件尺寸之误差来自于制程之变异,此变异往往呈现统计分布的型态,因此设计的公差规格常被视为统计型态。 ?统计公差方法的思想是考虑零件在机械加工过程中尺寸误差的实际分布,运用概率统计理论进行公差分析和计算,不要求装配过程中100 %的成功率(零件的100 %互换) ,要求在保证一定装配成功率的前提下,适当放大组成环的公差,降低零件(组成环) 加工精度,从而减小制造和生产成本。 ?在多群数据的线性叠加运算中,可以进行叠加的是『变异』值。 四.方和根法 计算公式（平方相加开根号） 假设每个尺寸的Ppk 指标是1.33并且制程是在中心
多元统计分析方法 Document serial number【UU89WT-UU98YT-UU8CB-UUUT-UUT108】
多元统计分析概述 目录 一、引言 (3) 二、多元统计分析方法的研究对象和主要内容 (3) 1.多元统计分析方法的研究对象 (3) 2.多元统计分析方法的主要内容 (3) 三、各种多元统计分析方法 (3) 1.回归分析 (3) 2.判别分析 (6) 3.聚类分析 (8) 4.主成分分析 (10) 5.因子分析 (10) 6. 对应分析方法 (11) 7. 典型相关分析 (11) 四、多元统计分析方法的一般步骤 (12) 五、多元统计分析方法在各个自然领域中的应用 (12) 六、总结 (13) 参考文献 (14) 谢辞 (15)
一、引言 统计分布是用来刻画随机变量特征及规律的重要手段，是进行统计分布的基础和提高。多元统计分析方法则是建立在多元统计分布基础上的一类处理多元统计数据方法的总称，是统计学中的具有丰富理论成果和众多应用方法的重要分支。在本文中，我们将对多元统计分析方法做一个大体的描述，并通过一部分实例来进一步了解多元统计分析方法的具体实现过程。 二、多元统计分析方法的研究对象和主要内容 （一）多元统计分析方法的研究对象 由于大量实际问题都涉及到多个变量，这些变量又是随机变量，所以要讨论多个随机变量的统计规律性。多元统计分析就是讨论多个随机变量理论和统计方法的总称。其内容包括一元统计学中某些方法的直接推广，也包括多个随即便量特有的一些问题，多元统计分析是一类范围很广的理论和方法。 现实生活中，受多个随机变量共同作用和影响的现象大量存在。统计分析中，有两种方法可同时对多个随机变量的观测数据进行有效的分析和研究。一种方法是把多个随机变量分开分析，一次处理一个随机变量，分别进行研究。但是，这样处理忽略了变量之间可能存在的相关性，因此，一般丢失的信息太多，分析的结果不能客观全面的反映整个问题，而且往往也不容易取得好的研究结论。另一种方法是同时对多个随机变量进行研究分析，此即多元统计方法。通过对多个随即便量观测数据的分析，来研究随机变量总的特征、规律以及随机变量之间的相互
七、灌注桩 （1）打孔沉管灌注桩单打、复打：计量单位：m3 V=管外径截面积×（设计桩长+加灌长度） 设计桩长——根据设计图纸长度如使用活瓣桩尖包括预制桩尖，使用预制钢筋混凝土桩尖则不包括加灌长度——用来满足砼灌注充盈量，按设计规定；无规定时，按0.25m计取。 （2）、夯扩桩：计量单位：m3 V1（一、二次夯扩）=标准管内径截面积×设计夯扩投料长度（不包括预制桩尖） V2（最后管内灌注砼）=标准管外径截面积×（设计桩长+0.25） 设计夯扩投料长度——按设计规定计算。 （3）钻孔混凝土灌注桩 成孔工程量，计量单位：m3 钻土孔V=桩径截面积×自然地面至岩石表面的深度； 钻岩孔V=桩径截面积×入岩深度度 混凝土灌入工程量，计量单位：m3V=桩径截面积×有效桩长，有效桩长设计有规定按规定，无规定按下列公式： 有效桩长=设计桩长（含桩尖长）+桩直径 设计桩长——桩顶标高至桩底标高 基础超灌长度——按设计要求另行计算。 泥浆运输工程量：计量单位：m3，工程量按成孔工程量计取。 八、人工挖孔桩 （1）、人工挖孔工程量：计量单位：m3 V（人工挖土）=护壁外围截面积×成孔长度成孔长度——自然地坪至设计桩底标高 V（淤泥、流砂、岩石）=实际开挖（凿）量 （2）砖、混凝土护壁及灌注桩芯混凝土工程量：计量单位：m3工程量按设计图示尺寸的实体积 九、水泥搅拌桩、粉喷桩，以立方米计算 V=（设计桩长+500MM）×设计桩截面面积（长度如有设计要求则按设计长度）。双轴的工程量不得重复计算，群桩间的搭接不扣除。 十、长螺旋或旋挖法钻孔灌注桩，以立方米计算 V=（设计桩长+500MM）×设计桩截面面积或螺旋外径面积（长度如有设计要求则按设计长度）。 十一、基坑锚喷护壁成孔及孔内注浆。 按设计图纸以延长米计算 十二、护壁喷射混凝土 按设计图纸以平方米计算。 十三、砖基础计算规则 1、基础与墙身（柱身）的划分： （1）基础与墙（柱）身使用同一种材料时，以设计室内地面为界（有地下室者，以地下室 室内设计地面为界），以下为基础，以上为墙（柱）身。 （2）基础与墙身使用不同材料时，位于设计室内地面﹢300MM以内时，以不同材料为分界线，超过﹢300MM时，以设计室内地面为分界线。 （3）砖、石围墙，以设计室外地坪为界线，以下为基础，以上为墙身。 2、砖基础的计算方法（计价表规则） （1）砖基础不分墙厚和高度，按图示尺寸以m3计算。其中基础长度：外墙墙基按外墙的中心线计算；内墙墙基按内墙基最上一步的净长线计算。 （2）不扣除的部分：基础大放脚T形接头处的重叠部分，嵌入基础内的钢筋、铁件、管道、基础防潮
一、双代号网络图6个时间参数的计算方法（图上计算法） 从左向右累加，多个紧前取大，计算最早开始结束； 从右到左累减，多个紧后取小，计算最迟结束开始。 紧后左上-自己右下=自由时差。 上方之差或下方之差是总时差。 计算某工作总时差的简单方法：①找出关键线路，计算总工期； ②找出经过该工作的所有线路，求出最长的时间 ③该工作总时差=总工期-② 二、双代号时标网络图 双代号时标网络计划是以时间坐标为尺度编制的网络计划，以实箭线表示工作，以虚箭线 表示虚工作，以波形线表示工作的自由时差。 双代号时标网络图 1、关键线路 在时标双代号网络图上逆方向看，没有出现波形线的线路为关键线路（包括虚工作）。如图中①→②→⑥→⑧ 2、时差计算 1）自由时差 双代号时标网络图自由时差的计算很简单，就是该工作箭线上波形线的长度。 如A工作的FF=0，B工作的FF=1 但是有一种特殊情况，很容易忽略。
如上图，E工作的箭线上没有波形线，但是E工作与其紧后工作之间都有时间间隔，此时E工作 的自由时差=E与其紧后工作时间间隔的最小值，即E的自由时差为1。 2）总时差。 总时差的简单计算方法： 计算哪个工作的总时差，就以哪个工作为起点工作（一定要注意，即不是从头算，也不是 从该工作的紧后算，而是从该工作开始算），寻找通过该工作的所有线路，然后计算各条线路的 波形线的长度和，该工作的总时差=波形线长度和的最小值。 还是以上面的网络图为例，计算E工作的总时差： 以E工作为起点工作，通过E工作的线路有EH和EJ，两条线路的波形线的和都是2，所以此时E 的总时差就是2。 再比如，计算C工作的总时差：通过C工作的线路有三条，CEH，波形线的和为4；CEJ，波 形线的和为4；CGJ，波形线的和为1，那么C的总时差就是1。
各种图形体积计算公式-1-
土建工程工程量计算规则公 式汇总 平整场地: 建筑物场地厚度在±30cm以内的挖、填、 运、找平. 1、平整场地计算规则 （1）清单规则：按设计图示尺寸以建筑物首层面积计算。 （2）定额规则：按设计图示尺寸以建筑物首层面积计算。 2、平整场地计算方法 （1）清单规则的平整场地面积：清单规则的平整场地面积＝首层建筑面积 （2）定额规则的平整场地面积：定额规则的平整场地面积＝首层建筑面积 3、注意事项 （1）、有的地区定额规则的平整场地面积：按外墙外皮线外放2米计算。计算时按外墙外边线外放2米的图形分块计算，然后与底层建筑面积合并计算；
或者按“外放2米的中心线×2=外放2米面积”与底层建筑面积合并计算。这样的话计算时会出现如下难点： ①、划分块比较麻烦，弧线部分不好处理，容易出现误差。 ②、2米的中心线计算起来较麻烦，不好计算。 ③、外放2米后可能出现重叠部分，到底应该扣除多少不好计算。 （2）、清单环境下投标人报价时候可能需要根据现场的实际情况计算平整场地的工程量，每边外放的长度不一样。 大开挖土方 1、开挖土方计算规则 （1）、清单规则：挖基础土方按设计图示尺寸以基础垫层底面积乘挖土深度计算。 （2）、定额规则：人工或机械挖土方的体积应按槽底面积乘以挖土深度计算。槽底面积应以槽底的长乘以槽底的宽，槽底长和宽是指混凝土垫层外边线加工作面，如有排水沟者应算至排水沟外边线。排水沟的体积应纳入总土方量内。当需要放坡时，应将放坡的土方量合并于总土方量中。 2、开挖土方计算方法
（1）、清单规则： ①、计算挖土方底面积： 方法一、利用底层的建筑面积+外墙外皮到垫层外皮的面积。外墙外边线到垫层外边线的面积计算（按外墙外边线外放图形分块计算或者按“外放图形的中心线×外放长度”计算。） 方法二、分块计算垫层外边线的面积（同分块计算建筑面积）。 ②、计算挖土方的体积：土方体积＝挖土方的底面积*挖土深度。 （2）、定额规则： ①、利用棱台体积公式计算挖土方的上下底面积。 V=1/6×H×(S上+ 4×S中+ S下)计算土方体积（其中，S上为上底面积，S中为中截面面积，S下为下底面面积）。如下图 S下＝底层的建筑面积+外墙外皮到挖土底边线的面积（包括工作面、排水沟、放坡等）。 用同样的方法计算S中和S下 3、挖土方计算的难点
柱下条形基础简化计算及其设计步骤 提要：本文对常用的静力平衡法和倒梁法的近似计算及其各自的适用范围和相互关系作了一些叙述，提出了自己的一些看法和具体步骤，并附有柱下条基构造表，目的是使基础设计工作条理清楚，方法得当，既简化好用，又比较经济合理。 一、适用范围: 柱下条形基础通常在下列情况下采用： 1、多层与高层房屋无地下室或有地下室但无防水要求，当上部结构传下的荷载较大，地基的承载力较低，采用各种形式的单独基础不能满足设计要求时。 2、当采用单独基础所需底面积由于邻近建筑物或构筑物基础的限制而无法扩展时。 3、地基土质变化较大或局部有不均匀的软弱地基，需作地基处理时。 4、各柱荷载差异过大，采用单独基础会引起基础之间较大的相对沉降差异时。 5、需要增加基础的刚度以减少地基变形，防止过大的不均匀沉降量时。 其简化计算有静力平衡法和倒梁法两种，它们是一种不考虑地基与上部结构变形协调条件的实用简化法，也即当柱荷载比较均匀，柱距相差不大，基础与地基相对刚度较 件下梁的计算。 二、计算图式 1、上部结构荷载和基础剖面图 2、静力平衡法计算图式 3. 倒梁法计算图式 三、设计前的准备工作 1. 确定合理的基础长度 为使计算方便，并使各柱下弯矩和跨中弯矩趋于平衡，以利于节约配筋，一般将偏心地基净反力(即梯形分布净反力)化成均布,需要求得一个合理的基础长度.当然也可直接根据梯形分布的净反力和任意定的基础长度计算基础. 基础的纵向地基净反力为： j j i p F bL M bL min max =±∑∑62