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. J

    Is the column space of a matrix always a full span in practice?

    In my lecture notes, the lecturer describes the column space of matrix A as the vector space spanned by the columns of A (which means that it is assumed that the columns of A are basis ) Is this true only in theory ?
  2. T

    Pressure gauge submerged in a fluid column

    Homework Statement What reading will we see on a pressure gauge that is at the middle and bottom of a fluid column? and why Homework Equations P=pgh where p is density and P is pressure The Attempt at a Solution Well according to the equations as the gauge drop lower and lower it...
  3. M

    Column Space of A'*A: Subset of A'?

    Let A be an n x p matrix with real entries and A' be its transpose. Is the column space of A'*A the same as the column space of A'. Obviously, the column space of A'*A is a subset of the column space of A' but can I show the other way? Thanks!
  4. F

    Determinants from any row or column

    I'm having a problem with this rule in general. Apparently one can calculate the determinant by multiplying the cofactors and entries of any row or any column of a matrix. I have a negative that pops up. I'll take a 3X3 matrix for simplicity. A= |a b c| |d e f| |g h i|...
  5. N

    Proving row space column space

    A , B are nXn matrices and AB=(A)^t t-is transpose prove that the space spanned by A's row equals the space spanned by A's columns i know that there dimentions are equals so in order to prove equality i need to prove that one is a part of the other how to do it? each column i of...
  6. Shackleford

    Row and column matrix operations

    Are you allowed to mix and match row and column operations? For (a), using only row operations, I cannot get the matrix into the form they want. Could I swap a few of the columns around to do so? For (b), I got it into the form they want. The rank of the matrix is 2 because I have I2 there...
  7. M

    Prove the column space of AB is contained in the column space of matrix A

    lets assume the matrix multiplication AB exists, how would i prove that the column space of AB is contained in the column space of matrix A? i know there is a theorem that says something like: "a system of linear equations Ax=b has solutions if and only if b is in the column space of A" Am...
  8. M

    Expressing Matrix Product Ax as Linear Combination of Column Vectors in A

    I want to express the matrix product Ax as a linear combination of the column vectors in A. I know for that for (2,3;-1,4)(1;2) i just row reduce the 2 previous matrices and then the solutions give the multiples needed for each column. How would i go about solving a similar problem but...
  9. M

    Determine whether the span of the column vectors of the given is in .?

    Determine whether the span of the column vectors of the given is in...? Homework Statement determine whether the span of the column vectors of the given matrix is in euclidean space R=4 1 0 1 -1 0 -1 -3 4 1 0 -1 2 -3 0 0 -1 this question is under the inverse of square...
  10. N

    Sources Of Error: closed air column

    I did an experiment in class to determine the speed of sound. I used the speed of sound in air equation with the room temp at 28°C which was calculated at 348.6m/s. However when doing the experiment I got 329m/s. I just want to know some source of error that may have caused this? I have...
  11. T

    Calc. Capacity Reduct. Factor for Masonry Column in Task 4

    calculate the capcity reduction factor for the column in task 4 based on your knowledge of column buckling. task4: a soild masonry column is 2.9m in height with a cross section of 270mm x 480mm. a single roof beam is the only connection at the top of the column, it provides enhanced...
  12. T

    Column space of positive semidefinite matrix

    how to prove that R(A)=\text{sum of} N(A-\lambda I)? \lambda is nonzero eignevalues of A
  13. L

    Is a Matrix with a Zero Column Invertible?

    Can a square matrix with a column of all zero's be invertible?
  14. W

    Replacing column by equivalent force and couple

    The Problem I've been given the beam shown below to carry out the Hardy Cross method (Moment Distribution) too. I have no problems with the method but I'm struggling with part b, which states "Replace column by an equivalent force and couple at point C"...
  15. R

    Properties Of Matrices with the same Column Space

    Homework Statement Suppose that A and B are 5 x 5 matrices with the same Column Space (image). (a) Must they have the same columns? (b) Must they have the same rank? (c) Must they have kernels of the same dimension? (d) Must they have the same kernel? (e) If A is invertible, must B be...
  16. N

    What is a pivot column in a system of linear equations?

    Homework Statement What is a pivot column?Homework Equations The Attempt at a Solution I tried google for some examples but I cannot find any. I need to know what exactly a pivot column is because I am trying to do a Linear Algebra problem about consistency and inconsistency. Can anyone...
  17. K

    Mathematica Mathematica: Change the data from column to row

    Hi, I have put my data in column form ( a large number of data) in Notepad. I have attached example of the data. I know how to import it into Mathematica. However I face the problem to change the whole set of data to row form in Mathematica so that I can plot the histogram in Mathematica. Thanks.
  18. Femme_physics

    What is the Column Effect in Trusses?

    What's the "column effect"? Reading about trusses, it says I'm not sure what's the "column effect". There's no wiki entry and Google seems to show me many results that don't provide the definition...
  19. M

    Matrix proof - augmented matrix - row reduction - column operation - proof

    Homework Statement If we let A be the augmented m x (n + 1) matrix of a system of m linear equations with n unknowns Let B be the m x n matrix obtained from A by removing the last column. Let C be the matrix in row reduced form obtained from A by elementary row operations...
  20. R

    Equivalent length of of column ?

    Equivalent length of of column ?? Homework Statement A Mild steel column has a cross section of 100 mm by 50 mm . Assuming a safety factor of 6 calculate the load that it can safely support? Homework Equations Rankines formula : W = Oc/K[1+a(AEe^2/I] The Attempt at a Solution...
  21. Q

    How are column operations used to obtain Q in elementary column operations?

    I'm reading Charles G. Cullens' "Matrices and Linear Transformations" and have a question about one of the examples. Don't worry- I'm self-studying this. Homework Statement This is the section about matrix equivalence- both row and column equivalence. It says "Theorem 1.30 If a sequence of...
  22. I

    Expansion of an aluminum support column under heart

    Homework Statement OMG, Embarrassing typo ^ *HEAT not HEART. :) Sorry! In any case, A construction worker uses a steel tape to measure the length of an aluminum support column. If the measured length is 18.6 m when the temperature is 21.2 C, what ist he length when the temperature rises to...
  23. R

    Column Space Basis: Why Does Row Reduction Work?

    I am a bit puzzled by the following. You know how they teach you that in order to find column space you just need to row reduce the matrix, look at the columns with leading 1's in them and then just read off those columns from the original matrix? Well, why does that actually work? I'm trying to...
  24. F

    Matrices Column Rearanging

    Homework Statement The actual problem is Find a basis for the null-space of the matrix (1 0 1 2 1) (0 1 2 0 1) (0 1 -1 3 1) Homework Equations there are no relevant equations. The Attempt at a Solution I attempted to get the matrix into RREF i got (1 0 3 0 1)...
  25. U

    A vibrating column with a critical load exerted on it

    I was wondering the critical load vary as a result of forced vibration? Intuitionally, I thought the critical load reduced. But how to show it analytically, Any idea?
  26. Z

    Exploring the Possibility of a Liquid Column: Refer Figure

    Homework Statement This question is a product of my own mind- Refer Figure. Suppose the value of P= 2Patm, can 2Patm fall to Patm before the liquid levels with the hole-level? In other words, can there be a liquid column above the hole?
  27. E

    Is my eccentrically loaded column design safe and efficient?

    My problem is proving my structure is sound. Currently i want to know my deflection from my loads applied. See attachment. My load is 4000 lb. My carriage weight is 1200 lb. My upright column or tube is a 6" x 4" x 1/4" structural steel which i have 2 of these. I have distances to my CoG...
  28. O

    How do you get rref with a variable in the last column?

    I'm trying to figure out how to set up a matrix where I don't know the last value ex a+2+4=x, b+4+6=x, c+2+6=x. Would it be something like this? [1,0,0,x-6] [0,1,0,x-10] [0,0,1,x-8]
  29. V

    What is a column n-tuple?

    Yet another silly question from me :/. From an instructor's notes: "Let V = R^n be the vector space of column n-tuples of real numbers." Not quite sure what the "tuple" means. For R^3, would an example be the transpose of (1,2,3)? Thanks in advance for responding. While we're at it, any...
  30. E

    Velocity of sound in air in a closed air column

    Am I missing something and doing this all wrong? Experiment and data: The level of water in the glass tube was adjusted by raising the supply tank until the sound from the tuning fork was at its loudest. This level corresponds to first resonance position and it was recorded. The...
  31. M

    Finding density of air in air column from just pressure?

    Homework Statement This is for a lab I finished but cannot get this question, I spoke with the TA today and she made it make sense but I am still not getting the question correct. (2) The difference in pressure between the lowest and the highest measurement point is related to the weight of...
  32. H

    Finding the height of a column of mercury

    Homework Statement The U-shaped tube in the figure has a total length of 1.0 m. It is open at one end, closed at the other, and is initially filled with air at 20C and 1.0 atm pressure. Mercury is poured slowly into the open end without letting any air escape, thus compressing the air. This is...
  33. R

    Stress in Reinforced Concrete Column

    When we calculate the stresses in the section of a Reinforced Concrete column reinfored with Steel Rods, it is seen that the percentage Load carried by the Steel is much greater than the percentage area it contributes in the cross sectional area of the reinforced concrete section. The load...
  34. S

    Formula for Vertical column +eccentric loading

    hi, can anyone help me with the formula for a vertical Column (C-Channel) subjected to Eccentric Loading? Regards, Subbby
  35. D

    What is a basis for the row, column, and null space of matrix A?

    Homework Statement Consider the matrix A: 1 4 5 0 9 3 -2 1 0 -1 -1 0 -1 0 -1 2 3 5 1 8 (Sorry I don't know how to do TeX matrices on this site) Find a basis for the row, column, and null space. Homework Equations The Attempt at a Solution I reduced to row echelon form, which...
  36. J

    Wavelength of sound waves and speed of sound in air column

    [b]1. You perform an experiment with a long column of air and a tuning fork. The column of air is defined by a very long vertical plastic tube with a circular cross section; the upper end of the tube is open to the outside air and the lower end of the tube is filled with water. The column of air...
  37. S

    Column swap in an augmented matrix

    This may seem like a very obvious question, but I thought it may be some sort of trick that my lecturer thought I may overlook... Well, when swapping columns of an augmented matrix, the solution set is unchanged (as long as you don't swap the 'b' column) is this correct? It is only swapping the...
  38. S

    What is the failure mode for a vertical pole with guy ropes?

    Hi, Thank you for taking the time to look at my problem. I am considering a vertical pole fixed in the ground at the bottom and experiencing a horizontal point load at the top. This pole is fixed with guy ropes from the top to the ground at a certain angle. See attached image. Assuming...
  39. D

    Linear Algebra Question: Matrix multiplied by a column of its inverse

    X is a 10x10 matrix what is X*[7th column of X's inverse]? thanks for any help you can provide!
  40. S

    Howto define the Column space of nxn matrix

    Homework Statement I thought that if you have a square matrix then the column space is the set of all linear independent vectors which can be written as a linear combinations of the others? Which inturn is the same as range of the Matrix? Am I wrong?
  41. S

    Mass of air in cylinder column

    Homework Statement The density of air in the lower atmosphere decreases exponentially with height: ρ = ρ0e−z/H where ρ0 = 1.3 kg/m3 and H = 10 km. What is the mass of air in a cylindrical column of cross-sectional area 1 m2 and height z, as a function of z? How much mass is contained in such...
  42. T

    Simple column buckling problem - pl help

    Knowing that the torsional spring is of constant K and that the rigid bar is of length L, determine the critical load P_{cr} beyond which the column would buckle. See pic for the problem. [As the spring uncurls, it applies moment K \theta to the bar.] The answer is P_{cr}=K/L
  43. X

    A column under thermal stress

    I have a problem with a constrained column under thermal stress where I am to find the reaction forces at the supporting ends of the column due to its own weight after being heated. Attached is the problem, equations used, and my solution attempt. I tried to solve for the reaction forces...
  44. H

    How to make a door that rotates around a column

    Hi there I'm a complete novice about this kind of thing, but I've decided to fulfil a long dream of mine and make a bookcase with a secret door in it :) I've thought about various methods, but eventually I've figured that the best system would be to make it rotate around a spindle on one...
  45. P

    Flip Columns in Origin - Bottom to Top?

    Can anyoune tell me how you flip a column in origin so you are reading it from bottom to top? I don't mind if it means making a new column. Or if this isn't possible then is it possible to do a differential when taking the bottom values first?? If that makes any sense Thanks
  46. E

    Can Column Vectors be Multiplied?

    Hello, Suppose that \mathbf{h} is an N\times 1 column vector. Can we say that: \mathbf{h}^*\mathbf{h}=\mathbf{h}\mathbf{h}^* where * means complex conjugate transpose? Thanks in advance
  47. Ranger Mike

    Help With Physics: Column Placement on Perfectly Level Floor

    Ok folks i thought i would use this forum for once. if i have a 2 foo by 2 foot by 10 foot long metal column and a perfect level floor, and place the column on end so it is 10 feet tall it should be pretty straight and square to the " perfect flat and level floor " surface..right! assume the...
  48. W

    Can a Complex Matrix X Solve the Column Subspace Problem?

    Let A_i (i=1,...,k) be a nonsingular complex matrix which size is M by M. The question is how to find a complex matrix X which size is M by N such that: span(A_1*X)=...=span(A_k*X) (I guess that there must be relations between M,N and k when nontrival solution exists. ) ask: 1)if non...
  49. V

    Linear Algebra - Column and Null Space - Take 2

    Homework Statement Ax=b where, A = 1 -1 ...-1 1 Homework Equations a) Find Null Space N(A) and Column Space C(A) b) For which vectors b does the system Kx=b have a solution? c) How many solution x does the system have for any given b The Attempt at a Solution a) For Null Space, I got x =...
  50. V

    Linear Algebra - Column and Null Space

    Homework Statement Ax=b where, A = 2 -1 ...-1 2 Homework Equations a) Find Null Space N(A) and Column Space C(A) b) For which vectors b does the system Kx=b have a solution? c) How many solution x does the system have for any given b? The Attempt at a Solution a) For Null Space, I...
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