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Building frames can be analyzed by various methods such as force method, displacement method, and approximate method. The method of analysis to adopt depends upon the types of frame, its configuration (portal bay or multi-bay) in multi-storied frame and degree of indeterminacy.
Building frames are the most common structural form that is encountered practically. Commonly, the building frames are designed in such a way that the beam-column joints stay rigid. A typical example of a building frame is the reinforced concrete multistory frames.
Analysis Methods for Buildings Frames
1. Force Method
- It is also called flexibility method or method of consistent deformation.
- Used to compute internal forces and reactions in statically indeterminate structures.
- It is suitable for analyzing statically indeterminate frames that have a single storey and uncommon geometry such as a gabled frame.
- Force method of frame analysis is dependent on transforming a given structure into a statically determinate primary system and calculating the magnitude of statically redundant forces required to restore the geometric boundary conditions of the original structure.
2. Displacement Method
This method requires writing the unknown displacements in terms of the loads using the load-displacement relationship. After that, solving the equilibrium equation for these displacements.
After the determination of displacements, the unknown loads are determined from the compatibility equations. All displacement methods follow this general procedure. In displacement method, three methods which are closely related to each other are presented:
2.1 Slope Deflection Method
- It can be used to analyze statically determinate and indeterminate beams and frames.
- In slope deflection method, it is assumed that all deformations are due to bending only; influences of axial and shear stresses are ignored.
- Another assumption is that all the joints of the frame are rigid, i.e, the angles between the members at the joints do not change, when the members of the frame are loaded.
2.2 Moment Distribution Method
- It is a method of successive approximation that may be conducted for any desired degree of accuracy.
- Basically, the method begins by assuming each joint of a structure fixed.
- After that, unlocking and locking each joint in succession, the internal moments at joints are distributed and balanced until the joints have rotated to their final position.
- A detailed discussion of moment distribution can be found here.
2.3 Direct Stiffness Method
- The direct stiffness method is a matrix analysis method which means equilibrium equations are formulated into a single matrix relationship.
- Free joint displacement equations can be automatically selected from the full system matrix and solved.
3. Approximate Methods
Approximate analysis is useful in determining (approximately) the forces and moments in the different members and in coming up with preliminary designs. Based on the preliminary design, a more detailed analysis can be conducted and then the design can be refined.
Approximate analysis is conducted by making realistic assumptions about the behavior of the structure. For analysis of frames subjected to vertical loads, points of inflection are used whereas portal method or cantilever method is used for frames subjected to horizontal loads
3.1 Portal Method
- It is used to analyze frames subjected to horizontal loads.
Assumptions made in portal method include:
- The points of inflection are located at the mid-height of each column above the first floor. If the base of the column is fixed, the point of inflection is assumed at mid-height of the ground floor columns as well; otherwise, it is assumed at the hinged column base.
- Points of inflection occur at mid-span of beams.
- Total horizontal shear at any floor is distributed among the columns of that floor such that the exterior columns carry half the force carried by the inner columns.
3.2 Cantilever Method
- This method is applicable to high rise structures.
The basic assumption of the method are:
- An inflection point occurs at the midpoint of each girder.
- An inflection point occurs at mid-height of each column.
- In a storey, the intensity of axial stress in a column is proportional to its horizontal distance from the center of gravity of all the columns in that storey
3.3 Points of Inflection Method
- This method is used to analyze frames subjected to vertical loads.
- The frame is reduced to a statically determinate form by introducing an adequate number of points of inflection.
- The loading on the frames is usually uniformly distributed loads.
- Assumptions used in this method include points of inflection located at 0.1L from both left support and right support, and axial forces in beams are negligible.
4. Kani’s Method
- It involves distributing the unknown fixed end moments of structural members to adjacent joints, in order to satisfy the conditions of continuity of slopes and displacements.
- The most important feature of Kani’s method is that it is self-corrective. Any error at any stage of iteration is corrected in subsequent steps.