Moment - Axial Force Interaction Report and Program

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1 oment - Aia Fore Interation Report and rogram ehdi Vojoudi Vojoudi@vojoudi.om THINK GLOBAL, ACT LOCAL Spring 3

2 Strutura Stabiity rojet. Sope Cauate the moment aia fore interation urve for a hinged oumn with variabe senderness λ, initia rooked w.. The end moments are and β. Conepts: a. Coumn setion profie is IB. b. Choose apaity urve from Chen of netherot urves.. Cauate every point of the interation urve aording to the ontat point of apaity urve and easti - urve.. oment equation At first we shoud find the oumn urvature differentia equation and then sove it to find the moment distribution aong the oumn member. So we draw a shemati view of oumn end onditions, urvature and oadings diretion Fig.. Fig. Coumn diagram

3 Strutura Stabiity rojet β w W tota But we know: w w W tota w w β & w w w β w w w β w w w 3 w. w. os. w 4. β 3 & 4 w w Soving the above equation: a. Soving the homogeneous equation w w wh os b. soving the no homogeneous equation: art I: art II:. w w w 3 4 os w w w 5

4 Strutura Stabiity rojet 3 art III: w w β w Assigning these three parts of answer by super position prinipe: os w os w os w w os 4 3 Then we put the resuts in differentia equation: os os w w β And the onstants C3 ~ C7 wi be β β 3 os os

5 Strutura Stabiity rojet E Then we assign these onstants in partiuar answer:. β w E p The genera soution are equa to summation of homogeneous and no homogeneous answers : w w w p h. os β w E The onstant vaues of C and C wi be auated by assigning the boundary onditions in the equation: os β w w β os Then the tota dispaement of the oumn wi be:. os os β β w E

6 Strutura Stabiity rojet 5 os β w os β. os E The tota urvature: os β w os E. And now we an find the moment in eah setion aording to the urvature of the oumn. w w. os β os E. β os os E. This moment equation wi be used to find the moment distribution aong the oumn.

7 Strutura Stabiity rojet 6 3. Capaity urves Chen and Netherot suggested two apaity equations: 3.. Chen 97 Chen suggested equation 3- where a, a and a 3 depend on the oumn setion profie and aso the numbers of the profie, but the average vaues are isted beow: a a a 3- Y Y 3 Wide fange profies bent on strong ae: Condition a a a <.5 Y < Y Wide profies bent on weak ae: Condition a a a 3.85 <.5 Y < Y 3.. Netherot 989 Netherot suggested another form of apaity urves that just differ in oeffiients. The average vaues are isted beow: Wide profies, bent on strong ae: Condition a a a 3.5 <. Y.5.5. < Y

8 Strutura Stabiity rojet 7 Wide profies, bent on weak ae: Condition a a a 3.5 <.447 Y < Y Note that in this urves the apaity of the setion is important and we don t are about buking beause buking ours in the member not setion. 4. Easti - urve The moment equation auated in setion wi be used to find the maimum moment in member depend on a speified end moment with varying from to y. Beause the hanges between and y, if the resuts be drawn it wi a Easti - urve as the moment are not greater than the yied moment. The agorithm for this proedure is simpe, just in two oops, the first for variations and the inner oop for variations aong the member from to L ength of the member. Further information on this agorithm wi be given in net setions. 5. Interation urve Interation urve wi be made by the /p and /y depends on the ontating point of Capaity urve and Easti - urves. Resuts of the auated urves are iustrated in setion 9.

9 Strutura Stabiity rojet 8 6. auation agorithm Chart 6- iustrates the agorithm diagram of the interation proedure. The initia vaues for and wi be very sma suh. and for wi be zero. Assign a vaue for Assign a vaue for Assign a vaue for Inrease Cauate the and find the aimum vaue of the Inrease YES If <L Inrease NO If ma/p ontats the apaity urve YES Save or ot /p and /y No YES If < p NO END Chart 6. auation agorithm

10 Strutura Stabiity rojet 9 7. Interation program soure The anguage of this program is Visua Basi, and beause this program an auate different materias, setions, oading onditions and different apaity urves it may be seem ompiated, but the main segment for auation is simpe. Here are the omments for different segments. 7.. Goba variabes definition In this segment the goba variabes defined and the omments for every variabe are in the beow. Setion roperties Dim Area As Singe Dim I As Doube Dim S As Singe Dim r As Singe ' Dim sngsender As Singe ateria roperties Dim intzigma As Integer Dim E As Doube End moment ratio Dim Beta As Doube Setion Area Setion oment of inertia Setion odue Gyration Senderness Yied Stress easti moduus end moment ratio Constant I 3.4 Dim I As Doube number of i 3.4 Capaity Curve arameters depend on what method seeted Chen pr Nether ot Dim CapaityA As Singe a for /y <.5 Dim CapaityA As Singe a Dim CapaityA3 As Singe a3 Dim CapaityA4 As Singe a for /y >.5 Dim CapaityA5 As Singe a Dim CapaityA6 As Singe a3 Dim CapaityLimit As Singe depend on the method the point of sope hanging.5 for Chen and. for Netherot ' auation parameters for inreag steps Dim inrease As Doube aia fore inreag step by : inrease * y Dim inrease As Doube oment inrease step by : inrease * p Dim Inrease As Doube X inrease for auation maimum of moment : inrease* ength

11 Strutura Stabiity rojet 7.. Information oeting After iking the Go bottom the information of the form wi be gathered by a proedure aed data. There is no auation is this proedure and just oet the data from the form and assign the vaues to variabes aording the seeted methods and vaues. Sub data Seeting the Setion properties Seet Case List.ListInde Case IB Area 6 I 45 S 89.9 r 4.6 Case IB Area 34 I 864 S 44 r 5.4 Case IB 4 Area 43 I 5 S 6 r 5.93 Case 3 IB 6 Area 54.3 I 49 S 3 r 6.78 Case 4 IB 8 Area 65.3 I 383 S 46 r 7.66 Case 5 IB Area 78. I 57 S 57 r 8.54 Case 6 IB Area 9 I 89 S 736 r 9.43 Case 7 IB 4 Area 6 I 6 S 938 r.3 Case 8 IB 6 Area 8 I 49 S 5 r.

12 Strutura Stabiity rojet Case 9 IB 8 Area 3 I 97 S 38 r. Case IB 3 Area 49 I 57 S 68 r 3 End Seet seeting the senderness of oumn sngsender CSngTet4.Tet Yied stress intzigma CIntTet.Tet Easti oduus E CDbTet3.Tet Reading Beta from form Beta CDbTet.Tet hoog the Capaity Curvetur If Option.Vaue True Then CHEN CapaityA CapaityA.378 CapaityA3 CapaityA4.3 CapaityA5.85 CapaityA6.5 CapaityLimit.5 Ese End If CapaityA CapaityA.5 CapaityA3 CapaityA4.5 CapaityA5 CapaityA6.5 CapaityLimit. auation parameters inrease CDbTet7.Tet inrease CDbTet8.Tet Inrease CDbTet9.Tet End Sub Nether ot 7.3. Cauation This is the main proedure of the program, the struture are simiar to the auation agorithm.

13 Strutura Stabiity rojet Go bottom proedure: rivate Sub Command_Cik Ca data ' oet the information from the form Definition the oa variabes Dim Length As Doube ength of the oumn Dim oo As Doube / Dim y As Doube Yied Aia Fore Yied Stress σ * Area of setion Area Dim y As Doube Yied oment Yied Stress σ * odue of setion S Dim p As Doube asti oment.5 * y Dim As Doube variabe for aia fore Dim As Doube variabe for Dim As Doube variabe for ength of the oumn Dim oment As Doube variabe for moment in the position Dim ma As Doube aimum oment of oumn Dim e As Doube Euer Fore Dim strp As String Dim strm As String Dim a As Doube Dim b As Doube Output string that ontains the /y vaues Output string that ontains the /p vaues An auiiary variabe An auiiary variabe Setting the variabes vaue I 3.4 Length sngsender * r auating the ength of the oumn y intzigma * Area e I ^ * E * I / Length / Length y intzigma * S p.5 * y strp "" strm "" iture.drawwidth sets the dispay monitor properties Start of auation of interation urves. initia vaue for First Loop Do Whie <.5 * y. Initia vaue for Seond oop Do Whie < y oo / E / I ^.5.5 * Length ma Third Loop Do Whie < Length oment Beta - Cosoo * Length * * Sinoo * / Sinoo * Length * Cosoo * / - / e *. * Length * SinI * / Length If oment > p Then GoTo Cheks not to do unneessary auation If ma < oment Then ma oment End If Inrease * Length Loop Inreag

14 Strutura Stabiity rojet 3 Compare the ma with Capaity urve Chen or nether ot and If / y < CapaityLimit Then If Absma / y -.5 * CapaityA3 - CapaityA * / y - CapaityA * / y ^ <.5 Then iture.set / y /.5 * iture.width *.95, - / y * iture.height, a / y b / y /.5 strp strp CStra Chr3 Chr strm strm CStrb Chr3 Chr End If Ese If Absma / y -.5 * CapaityA6 - CapaityA4 * / y - CapaityA5 * / y ^ <.5 Then iture.set / y /.5 * iture.width *.95, - / y * iture.height, a / y b / y /.5 strp strp CStra Chr3 Chr strm strm CStrb Chr3 Chr End If End If inrease * y Loop inrease * p inreag rogressbar.vaue / p * Loop Inreag Tet5.Tet strp Tet6.Tet strm End Sub Write the out put Write the out put

15 Strutura Stabiity rojet 4 8. How to use rogram Interation program is simpe to use and the form is designed user friendy. The different parts of information divided, the best and ommon vaues are defaut and an be hanged. Fig 8. Fig 8. rogram appearane 8. Shemati diagram This is a shemati diagram for oading ondition and end hinges. The β variabe an be entered here.

Strutura Stabiity rojet 5 Loading Diretions Enter the β here Fig 8. shemati diagram of oading onditions 8. Setion properties The setion size and senderness an be seeted here, fig 8.3. Figs 8.

16 Strutura Stabiity rojet 5 Loading Diretions Enter the β here Fig 8. shemati diagram of oading onditions 8. Setion properties The setion size and senderness an be seeted here, fig 8.3. Figs 8.3 seet the rofie size and senderness 8.3 ateria properties You an enter the materia properties suh as yied stress and easti modue it the speified paes, Fig 8.4. Fig 8.4 ateria properties 8.4 Cauation parameters The inreag steps for, and an be defined and hanged here. Note that the steps infuene the auray of the resuts.

Strutura Stabiity rojet 6 Fig 8.5 inreag steps 8.5 Capaity equation The apaity equation an be seeted here to be used in auations. The seetabe equations are Chen 97 and Nether ot 989.

17 Strutura Stabiity rojet 6 Fig 8.5 inreag steps 8.5 Capaity equation The apaity equation an be seeted here to be used in auations. The seetabe equations are Chen 97 and Nether ot 989. The apaity urve wi be potted by iking the DRAW bottom. Draw the Capaity urve Fig 8.6 Capaity equation seetion 8.6 Go bottom This bottom, starts the auation of the interation urve and by auating eah point, it wi be potted on the dispay monitor. Fig 8.7 Go bottom to start the auation 8.7 rogress bar During the auation, this wi show the progress. Fig 8.8 rogress bar 8.8 Resuts There are two oumns that show the resuts of auation for /y and /p that an be easiy seeted or printed.

18 Strutura Stabiity rojet 7 Fig 8.9 Resuts 8.9 Dispay monitor Dispays a shemati pot of resuts, It an be eared and the bak oor an be hanged Fig 8. Dispay monitor

19 Strutura Stabiity rojet 8 9. Resuts The resuts for senderness equa to zero,,4,6,8, and are shown in fig 9. to fog 9.7. Note that in Senderness equa to zero the interation urve is the same for apaity urve. The resuts are for defaut vaues. Senderness ~ Fig 9. Senderness Fig 9.

20 Strutura Stabiity rojet 9 Senderness Fig 9.3 Senderness Fig 9.4

21 Strutura Stabiity rojet Senderness Fig 9.5 Senderness Fig 9.6

22 Strutura Stabiity rojet Senderness Fig 9.7

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