In the past and in the ~early~ post-war period, they were essentially systems that provided lateral stability to tall buildings. rigid structural frc, mes. Since the wall can take care of most of the subsequent elements coming into the structure, it is therefore called a shear wall. When the frame part of the building is inherently quite stiff, the interaction between the shear wall and the frame can result in a significantly stiffer and more efficient design.
As a result, the frame cooperates more effectively in the upper portion of the building, where the lateral load shears are relatively smaller, and the shear wall carries most of the shear forces in the lower portion of the building, where it is located.
LITERATURE REVIEW
The detailed solution of some of the p~pera together with the corresponding figures is given in chapter chapter 3. If the shear of the frame is assumed to be constant, the system can be treated as a wall supported at the top by a spring. By solving the equation, the deviation of the system as well as the internal actions can be estimated.
The contribution of a single column to the 5A parameter of the equivalent crossbar is given by.
SCH)
CONCENTRHED LOAD P AT TOP OF STRLJCTIJ,~E
TRIANGULAR DISTRIBUTION
The moment of inertia of this system at each level is equal to the sum of the moments of inertia of all shear walls, regardless of their shape. The vertical movements of the connecting points with system Ware are calculated by multiplying the slope. a. The spring stiffness Kf is defined as the lateral point load applied to the top of the frame to cause deflection of the unit in its line of action.
If the rotation at the base of the shear wall is to be neglected, the term yw in equation C must be omitted.
7\ and L ~c' behavior CEin be discu ssed in terms of only two vari-
Introduction
The flexibility coefficients characterize the behavior of the structure by specifying its displacement response to applied forces at the coordinates, and the stiffness coefficients by specifying the forces required to produce given displacements at the coordinates. The solution of large building frames by the stiffness method uses a special technique by taking advantage of the sparse nature. The one bay frame analysis is further modified to take care of variable story heights, moments of inertia, crogs-.
Cornputer programs for all the above analyzes are developed and written in Fortran II and Fortran IV.
FRAME
4.3",1 ' STIFFNESS MATRIX OF THE FRAME
FRAME ANALYSIS (ONE BAY)
GENERAL ONE BAY FRAME ANALYSIS
522= EWA1!H+12EBI1/L13
546= -(12EBI2 / U3) ,
551= 6EWI2/H2 571=' 6EW13/H2
517, 10= (ZEWI1/H)51,10
COMPUTER PROGRAMS FOR STRUCTURES
Moreover, some of the variables in the program will be of integer type while others are of floating point type. IBf'l1 162.0 computer of I\tomic lnergy Center vJas used in the development 8th test run of ,11 the programs. To cite an example for a two-bay frame program, the compile time required by IBM 1620 is .L8 min".
10ment of inertia of left column (equ81 for all floors) Moment of inertia 0 f right column (equal for all floors ~. 34;lament of inertia of beam (equ81 for all floors) Cross-sectional area - left column (equal for Preparation of data for one truss. .al Number of floors of loaded floors, properties of elements, structure parameters and modulus of elasticity.. a) Floor level, loads applied to connections, loads at the end of confined elements due to loads .
While single frame program can be used for constant height of floor, constant moment of inertia of Beams etc. •• General program a CRn frame frame takes care of variable floor height, moment of inertia, area etc. is .. given in Table 5D and the data preparation is given in Table 5C,. Moment of inertia of the left column or wall Moment of inertia of the right column or wa~l.
10ment of Inertia of Beam Area of left column or wall Area of right column or wa~l. Floor height; Moment of inertia of left beams; real beams; left vertical members; center vertical members right vertical members etc.
FER(
Identifiers used in two variables of type Bay Frame Computer Program Integer are: - N. Preparation of data for two Bay ProgDaq j. ,J.
NSLOAD
N5LOAD,WI1,WI2
1oment of inertia of the right beam The span of the left beam .. and S5 are the same as the two-piece frame. Preparation of data for a general two-part framework program .. a) Loaded floor level, actions used on common b) Loaded floor level,. actions at the ends of attached members due to loads. a) Floor height, properties of vertical members. A GA for a one-piece frame was written to compare the actual value of the frame GA evaluated by the stiffness method and recursion.
The identifiers used in this program are the same as the identifiers of the first data card of a bey frame program. This program was written to find out the exact GA value, as well as H5M for two Bay frames. Identifiers used in this program are the same as the identifications of the first two cards of two bey frames, except that the identifications in this program are arranged in different ways.
The identifiers used in this program are the same as the .identifiers of the first two cards in the two-frame program. A tall building frame is one of the highly redundant structures encountered in the construction industry. Numerical solution of exact analysis; .It is too time-consuming and sometimes impossible without the help of fast digital computers. In this chapter we tried to compare different parameters or assumptions of the approximate method.
To compare the GA value with the Heidebrecht and Smith method (HS~1) and the exact method (EM) progrc,ms were developed for one bay and two bay frames. Similarly for a Bay frHme, the GA value can be used in the following floor ranges for different values of 7\.
GA FOR ONE BAY FRAME
GA FOR ONE BAY FRAME (CONTO.)
GA VALUE FOR TWO BAY FRAME
The third assumption for the portal method is: "The horizontal shear at each floor is distributed among the columns of that floor such that each inner column carries twice as much shear as each outer column." While the third assumption for the cantilever method J.S. "The intensity of the axial stress in each column of a story is proportional to the horizontal distance of the column from the centroid of all the columns of the story." under consideration". Several lateral loading programs with different structural data were run to check the validity of the above simplified version.
Analyzing the results, he found chat for symmetric Yrams, the assumptions j of the above methods hold for all values of 7\.., while assumption 2 does not hold; valid for any value of 7\. Amount; which causes the warp point in the columns to move off-center. You can estimate using the tables or graphs given after this section. If significant axial loads cause OCC1JT in the columns, • bending moae deformations become more pronounced Iz.
POINT OF INFLECTION AT COLUMN ------(ONE BAY FRAME)
NUMBER OF STOREY = 10 STOflEY
In one set the moment of inertia oY all the columns W.8re kept equal, while in the other set the moment of inertia of the inner column was kept double the moment of inertia of the outer. From the computer result, it is found that for the frames where the moment of inertia of inner column is double the moment of inertia of outer column, the assumptions 1 and 3 of portal and cantilever methods apply, The bending point at. For both exterior and interior columns, the inflection point is at the same level in a story.
For the frames where the moment of inertia of all columns is the same, only assumption 1 of the portal method and. The inflection point for exterior and interior columns on a floor do not fall on the Si3me level. Inflection point at column and ratio of column S~lear are shown in tabular form.
The area and moment of inertia of the inner column is twice that of the outer column Number of floor'= -20. FLEXION POINT AND SHEAR RATIO IN COLUMNS ~ INTERIOR AND INTERIOR COLUMNS All columns are of the same section. The moment of inertia of the connecting beam (lib) varied such that ~(= I£bh/lc.i) varied.
The vertical members of an o. of the frames are shear walls while the vertical number i. For all floors: Same as above except for the moment of inertia of the top floor beam.
PERCENTAGE OF SWAY REDUCTION WITH HEAVIER CROWN COUPLING BEAM
Several programs were run for a single-bay frame to find the percent load transfer from one column loaded with v8 to another column. Vb is the shear stiffness of the beam and is equal to 12EI/L3 (assume equivalent shear stiffness of the beam Cv c 1.0). For Vb/Vc from 0.1 to 1.Oj the maximum load transfer percentage is 1.0204%, which occurs within the three main floors.
CONCLUSIONS AND SUGGESTIONS
- One bey frame analysis
- I I,NSL
- J- I, 4 NN=4* ILS-1) +J
- AIIROW,L)
- J= I,N 17 IPVOT (J 1- 0
For a one-piece symmetrical frame, the inflection point is at the center of each beam and the total horizontal shear at each floor is distributed equally among the columns of that floor. In the 8 upper floors, the bend point is closer to the bottom of the column, and in the lower floors it is closer to the top of the column. In a two-piece symmetrical frame, the point of bending at the center of each beam is ~ I"f moment: v.
Pain+; of bending for both internal and external columns at one storey falls at the same level. For a symmetrical two-bay frame, if the moment of inertia of all columns is the same, the inflection point in the outer and inner columns at one floor does not fall at the same level. The following approximate analysis of long shear wall - frame structures m."3Ybe compared \-Jith uexi3ct" analysis to draw a conclusion as to which method of approximate analysis is most suitable for a particular structure.
Programs can be developed for multiple fr~mes and the validity of the assumptions of the portal and console methods can be verified. Gould, P.L •• "In eraction of Shear \-1all Frame Systems in Multistorey Buildings", Journal of the American Concrete. B., "Concrete Shear Walls Combined with Rigid Frames in Multistory Buildings Subject to Lateral Loads," A.Cr.
34;Interaction Between Shear Walls and Frames" Later~lly Loaded Systems Consisting of Walls and Frames. Clough R.'tJ., Wi.lson E.L., King J.P •• "Large Capacity multistorey Frame Analysis Programs~ Journal of the Structural Division, Amerikaanse Vereniging van Siviele Ingenieurs, Vol.
C PROGR~M CAN BE USED FOR FRAMING WALLS OR COLUMNS OR ALL C PROGRAM CAN ACCOUNT FOR VARIABLE HEIGHT, SPA~, MOMENT OF INERTIA.
