What is Column: Definition and 333 Discussions

A column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above to other structural elements below. In other words, a column is a compression member. The term column applies especially to a large round support (the shaft of the column) with a capital and a base or pedestal, which is made of stone, or appearing to be so. A small wooden or metal support is typically called a post, and supports with a rectangular or other non-round section are usually called piers.
For the purpose of wind or earthquake engineering, columns may be designed to resist lateral forces. Other compression members are often termed "columns" because of the similar stress conditions. Columns are frequently used to support beams or arches on which the upper parts of walls or ceilings rest. In architecture, "column" refers to such a structural element that also has certain proportional and decorative features. A column might also be a decorative element not needed for structural purposes; many columns are engaged, that is to say form part of a wall. A long sequence of columns joined by an entablature is known as a colonnade.

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  1. C

    Stress in a concrete support column

    Homework Statement As quoted from the question sheet: When building a tall support, often the self weight of the support must be considered. For an optimal support, the volume of material, and hence the cost, will be a minimum. If the maximum allowable stress in concrete is 12 MPa, determine...
  2. G

    Cross product of row and column vector

    For the two matrices A and B, (AB)i,j = ri . dj ---- . refers to dot product ---- ri is the ith row in A and dj is the jth column in B. Let us say that A and B are n x n system of column vectors. Then a row vector ri of A would correlate to a component vector of the sum of the column vectors...
  3. D

    [Linear Algebra] Nullspace equals Column space

    Homework Statement Why does no 3 by 3 matrix have a nullspace that equals its column space? Homework Equations NA The Attempt at a Solution A = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix} \] C(A) = \begin{bmatrix} 1 \\ 0 \\ 0...
  4. K

    Row total and column total puzzle

    Arrange the nine cells of a 3x3 square with digits from 1 to 9, with each digit occurring exactly once, such that: ## The respective totals of the first column, second column and the third column are 15, 19 and 11, and: ## The respective totals of the first row, second row and the...
  5. H

    Column Space and Pivot Columns in Reduced Matrices

    To find the column space of a matrix, you reduce the matrix and those columns that contains leading variables(pivot columns), refers to the columns in the original matrix who span the columnspace of the matrix. But does the pivotcolumns in the reduced matrix also span the column space of the...
  6. G

    Matrix, in which there is a column of 0's or a row of 0's

    Given an n x m matrix, in which there is a column of 0's or a row of 0's, would it be equivalent to write the matrix while neglecting the column or row of 0's?
  7. Q

    Calculating Resonant Frequencies of Closed Air Columns

    Homework Statement A closed air column is 60.0cm long. Calculate the frequency of the forks that will cause resonance at: a) the first resonant length b) the second resonant length Note that the speed of sound is 344m/s. Homework Equations Ln = (2n - 1) * \lambda / 4 fn =...
  8. J

    Design of Steel Bar Column <1sq, 6' Long; 30k psi Stress Limit

    a steel bar 1 " sauare 6 ' long is to be used as a column.ends are free to rotate put may not be displaced stress is limited to 30,000 psi. i believe my teacher expect conform code AISC.
  9. S

    Packed Absorption Column - Solving for min water rate and transfer units.

    Having much difficulty with the problem below. Any direction would be greatly appreciated. A waste gas stream contains .045 mole of ammonia per mole of carrier gas. Its desired to design an absorber using water which will reduce the ammonia concentration in the exit gas from the absorber to a...
  10. J

    Show that matrix AB has its row and column vectors in A and B

    Homework Statement Given matrices A and B, show that the row vectors of AB are in the row space of B an the column vectors of AB are in the column space of A Homework Equations Just matrix multiplication, reduced row echelon form, and leading one's for row and columns The Attempt at...
  11. M

    LaTeX Matrix Row & Column Labels in Latex

    Hello, I'm new to Latex and I'm having some problems creating a 5 x 5 matrix. I need to label each column 1 through 5 and I need to label each row 1 through 5. I need the row labels to be on the right side. I've found a couple of links online, but they only show how to label rows on the left...
  12. A

    How Do You Solve a Matrix Equation with Eigenvalues?

    Homework Statement Solve the matrix equation: [10 1 9 1 4 3 2 -1 3] X = 3X where X is a column matrix. Please show all the steps, thanks. The Attempt at a Solution I think the solution is X = kU, where k is any constant and U is the vector... yet not really sure how to...
  13. C

    How to delete column in notepad

    Hi, I was running a labview program and it wrote my data to an lvm file, which can be opened with notepad. The problem I am having is the way labview outputted my data. It has the time and the strain separated by a comma. I attached the file, so everyone can see. What I want to do is somehow...
  14. R

    Finding the Column Space of Matrix A

    Homework Statement We have a matrix A which row-reduces to: A = \left[\begin{array}{ccccc} 1&2&0&0\\ 0&0&1&0\\0&0&0&1 \end{array}\right] I'm asked to find the column space of A. Homework Equations The Attempt at a Solution I'm not sure what to write down for this...
  15. K

    What are the Water Heights for a Standing Wave in a Tuning Fork and Tube Setup?

    Homework Statement A 1.0m long vertical tube is filled with water. A tuning fork vibrating at 580Hz is held over the open top of the tube as the water is slowly drained from the bottom. At what water heights, measured from the bottom of the tube, will there be a standing wave in the tube...
  16. Q

    Null space and Column Space

    I am just wondering what is meant when someone says the Col A is a subspace of null Space of A. What can you infer from that? Also what is a null space of A(transpose)A How do they relate to A? Are there theorems about this that I can look up?
  17. J

    Dimension of row/ column space

    Homework Statement In the following exercises verify that the row rank is equal to the column rank by explicitly finding the dimensions of the row space and the column space of the given matrix. A = [1 2 1 ; 2 1 -1] Homework Equations The Attempt at a Solution All i can...
  18. J

    Column, Solution and Row Spaces

    Homework Statement A = [ 1 0 1 -1 1 -3 2 1 0] what is the column space of A? What is the row space of A What is the solution space of A? Also, if i were given a multiple choice, how do I check if a vector is in either the column, row or solution space of A ...
  19. O

    Are Column Vectors in AB Unchanged if Linearly Independent?

    If you have a 3x3 matrix AB of rank 2, and you are asked to find two linearly independent vectors in the column space of A, are those the same vectors in the column space of AB? I figure it is since if the vectors are linearly independent they wouldn't change. Am I right?
  20. J

    Structures. column theory, Buckling

    Homework Statement the question is in the picture. the rectangular steel bar shown supports a concentric load of 13000lbf. Both ends are fixed. If te modulus of elasticity is 29x10^6 lbf/in^2, what is the maximum length the rod can be without experiencing buckling failure? Homework...
  21. K

    How can I calculate the compression of a support column under a heavier weight?

    Homework Statement A support column is compressed 2.46 x 10^ -4m under a weight of 5.42 X 10^5N. how much is the column compressed under a weight of 4.8 X10^6N? Homework Equations F=KX The Attempt at a Solution By using that equation, I get 542000 = .000246K Solve for K, and I get a...
  22. F

    Does [2 15]T Lie in the Column Space of A?

    Homework Statement Does b = [ 2 15 ]T lie in the column of the matrix A [1 -3] [2 5] Homework Equations a basis of CS(U) forms a basis for the corresponding columns for CS(A) The Attempt at a Solution I reduced the given matrix into row echelon form and determined its column...
  23. I

    Can You Find a Matrix Where Column Space Equals Null Space?

    Hey fellas could use a hand on a linear question that has been bugging me. Give an example of a 4 x 4 matrix such that col A = nul A Appreciate any help! Thanks, ib
  24. F

    Basis for row and column space

    Homework Statement Can anyone help me figure out basis for RS(A) and basis for CS (A) along with their dimension? I mean dim CS(A) and dim RS(A) where A is [1 -2 4 1] [0 7 -15 -4] [0 0 0 0] Homework Equations The Attempt at a Solution are all non zero rows the basis for...
  25. F

    Understanding row and column space

    Understading row and column space Homework Statement I am having hard time trying to understand row and column space. Can anyone simplify the meanings of them so that i can visualize them well. Homework Equations dimension of row space = rank ? How? Why? The Attempt at a Solution...
  26. F

    Analyzing a Cylindrically Symmetric Plasma Column

    Homework Statement A cylindrically symmetric plasma column in a uniform B field (= B0 in z direction) has n(r) = n0 exp[-(r/r0)^2] and ni = ne = n0exp[e phi/kb Te] where phi is the potential and Te is the temp of the electrons. (a) Show that Ve and VDe are equal and opposite Homework...
  27. S

    Solving Column Reactions with an Offset Load

    A column AB is anchored to the ground by a pin-joint at A, and is held in a vertical position by various loads as shown. Determine: (i) Magnitude of force f1 (ii) Magnitude and direction of the reaction at A I know how to calculate F1 if it was on a horizontal or vertical. But I'm not sure...
  28. A

    Column of Mercury at Sea Level

    Homework Statement At sea level, the pressure of the standard terrestrial atmosphere will support a column of mercury of density 1.359 x 10^4 kg/m^3 and of height 0.7600m at a place where the acceleration due to gravity is 9.80665 m/s^2. Show that 1 atmosphere = 760 mm Hg = 1013hPa. I...
  29. A

    Adjusting Air Column Length with Water: Why No Waves?

    In many problems , to change the length of the air column we use water but I don't understand why waves don't pass into water and then the reflected wave will have less amplitude and hence standing waves could not be formed.
  30. Saladsamurai

    Understanding Column Vectors: A Physical Interpretation

    Column Vectors? Alrighty. I have a silly question about column Vectors. I first learned about the concept of a vector in Physics, i.e. position, velocity, acceleration, etc. so I easily understand the premise of a row vector. For example the matrix \left[\begin{array}{ccc}1 & 2 &...
  31. N

    LaTeX [Latex] Double -> Single Column

    Hi all, I have a class file template which uses double columns throughout. I wish to insert a table which will fill the entire page so I need to somehow break the two column format for a small section and then go back to it afterwards. Does anyone know how to do this? Thanks in...
  32. J

    What to do with a zero column in a system of linear equations?

    Hello, just started a LA course, and I have a small question. If I get a zero column while solving for a system of linear equations, and that column corresponds to, say, variable x_{5}, do we just not include it in the solution set since it appears in no equation of the system? Or is it a free...
  33. V

    Wavelength (Open Air Column)

    Hello there, For the following problem, I am arriving at an answer different from the given one so I would appreciate any help or hints. Thank you. My work is shown below. --- 1. A slightly smaller plastic pipe is inserted inside a second plastic pipe to produce an air column, open at both...
  34. C

    Possible Sources of Error in Speed of Sound Lab

    resonance in closed air column Homework Statement we have conduct a lab to determine the speed of sound and estimate room temprature by using open air column method. put a tube in the water, have a tuning folks (sound source) on the above, and pull the tube up and down to find the resonance...
  35. B

    Column space and kernel

    Homework Statement If col (A) is column space of A and ker(A) null space of A with ker(A) = {Ax = 0} and ker(A') = {A'y = 0} Homework Equations Consider the (3x2) matrix : A = [1,2 ; 3,4 ; 5,6] (matlab syntax) Show that col(A) = c1 * [1,0,-1]' + c2 * [0,1,2]' The Attempt...
  36. B

    Is b in the column space of A and is the system consistent?

    1. Homework Statement [/b] For each of the following choices of A and b, determine if b is the column space of A and state whether the system Ax=b is consistent A is a 2 by 2 matrix , or A=(1,2,2,4) , 1 and 2 being on the first row and 2 and 4 on the second row. and b=[4,8] 4 being on...
  37. N

    Placing 8 rooks onto a 8x8 chess board so no two share same row or column

    Homework Statement In how many ways can eight identical rooks be placed on an ordinary 8x8 chessboard so that no two are in the same row or column? In how many ways, if each rook has a different color? Homework Equations I looked at the equation n choose k (nck), but I don't know if...
  38. N

    Dimension of column- and rowspace

    [SOLVED] Dimension of column- and rowspace Homework Statement My book doesn't answer this question clearly, but I have notived the following connection: Does the dimension of the rowspace of a matrix equal the dimension of the columnspace of a matrix which equals the rank of the matrix?
  39. E

    Math behind tipping/toppling a column or vertical structure

    I want to know where to look for information relating to toppling. I have looked at stability of equilibrium but the real question is: If say for arguments sake, there is a column 2m high and 1/4m wide - it would be easy, if we knew the weight of the column, to establish the force required...
  40. R

    Product of column and row vectors

    Hi All, I need to multiply column and row vectors but not sure that I am doing this right (on the picture below): http://img244.imageshack.us/img244/6222/35459606ye4.th.jpg Could you check it and correct if necessary? Thank you.
  41. N

    Solve Column Space, Matrix Problem with (x,y,z,w)^T

    [SOLVED] Column space, matrix Homework Statement I have a linear transformation f from R^4 -> R^4 given by a matrix. I have to find the range of f(R^4) which containts the vector (x,y,z,w)^T. The Attempt at a Solution I know that the range of f is the column space, how do I make sure that...
  42. N

    Linear algebra and column spaces

    Homework Statement I have a linear transformation T which is associated with a matrix A. I want to find the image of T, which is given by the column space of A. I have done this. Now I have a vector B = (x,y,z,w)^T, and I want the vector B to be part of the image of T. To do this, I write...
  43. S

    Find the Second Resonant length of an air column

    Homework Statement Find the second resonant length of an air column that resonates with a sound of frequency 1.0 kHz at 15.0 degrees Celsius under each of the following conditions. a) the air column is closed at both ends b) the air column is open at both ends Homework Equations...
  44. H

    Zero determinant - Can we make a zero column?

    I just wanted to know that the following statement is always true or not. After I expand the determinant I get the value of the determinant as zero, ie. I know that the value of the determinant zero. Then with the help of row or column transformations can we transform the determinant into...
  45. M

    What is the stress within the column?

    Homework Statement A marble column of cross-sectional area 1.7 m2 supports a mass of 30,000 kg. (a) What is the stress within the column? (b) What is the strain? Elastic modulus for marble E (N/m^2) 50e9 shear modulus (G) Homework Equations a)stress=F/A=N/m^2 b) don't know...
  46. M

    Weight of 7 ft Water Column w/ Radius 1.1m

    Homework Statement What is the weight of a column of water 7 ft high with a radius of 1.1m? The density of the water is 1000 kg/m/m/m Answer in units of N.Homework Equations Volume = pi * r^2 * h 7 ft = 2.1336 m Weight = Volume * Density The Attempt at a Solution Volume = 3.14 * 1.1^2 *...
  47. T

    Help Solving Physics Problem: Air Column Frequency Overtones

    Hi, I'm new here, so I don't really know how this works, but if someone could help me solve this physics problem, that would be great! An air column open at both ends, has a fundamental frequency of 2000 Hz. What are the frequencies of the first two overtones? I have been stuck on...
  48. stewartcs

    Fluid Column Height Drop Due to Gravity

    How far will a column of a fluid with density p1 fall if it is inside of a tube (open to atmosphere at the top), inwhich the tube is inside of a tank of another fluid with density p2 (p1 >> p2)? Assuming that the tube was intially plugged at the bottom while filling it with the higher density...
  49. A

    Finding length of tube, air column, standing waves

    Homework Statement A 50-cm-long wire with a mass of 1.0 g and a tension of 440 N passes across the open end of an open-closed tube of air. The wire, which is fixed at both ends, is bowed at the center so as to vibrate at its fundamental frequency and generate a sound wave. Then the tube...
  50. 4

    Proving Theorem: Column Space of Matrix A is a Subspace of R^m

    How would I prove this theorem: "The column space of an m x n matrix A is a subspace of R^m" by using this definition: A subspace of a vector space V is a subset H of V that has three properties: a) the zero vector of V is in H. b) H is closed under vector addition. c) H is closed under...
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