**Analysis Methods for Building Frames:**

The term analysis method for building frames of a is defined as a general flatāplate structural system comprising thin Kirchoff plates. Which are interconnected by oneādimensional flexural elements of various shapes and layouts.

**There are have many different methods of building frame analysis that’s are below-**

**Building Frames Analyze by Approximate Methods for Vertical Loads.****Building Frames Analyse by the Cantilever Method for Horizontal Loads.****Building Frame Analyses by the Portal Method for Horizontal Loads.**

**#1. Building Frames Analyze by Approximate Methods for Vertical Loads-**

- At first, we have to consider a building frame subjected to vertical loads.
- For easy to calculate the required three assumptions, we consider a simply supported beam.
- The first assumption is that for these cases, zero moments occur at the support of the beam.
- The second assumption of frame analysis is considered a fixed beam and a vertical load are subjected to it.

**#2. Building Frames Analyse by the Cantilever Method for Horizontal Loads-**

- During its lifetime of a building, a frame may be subjected and earthquake loads.
- In this method, the building frame must be designed to withstand lateral loads.
- A multi-story or two-story frame subjected to lateral loads and the actual deflection of the beam shows the dotted.

**#3. Building Frame Analyses by the Portal Method for Horizontal Loads-**

In this method of frame analyses, some assumptions have flowed below-

- In the portal method of frame analyses, each column an inflection point occurs at the mid-height.
- The interior column carries twice the shear of the exterior column, such as the total horizontal shear at each story is divided between the columns of the story.

## Frame Analysis-

The frame analysis is the members and structure at working loads, and elastic analysis deals with the study of strength and nature.

The frame analysis is defined as a general flatāplate structural system comprising thin Kirchoff plates. Which are interconnected by oneādimensional flexural elements of various shapes and layouts.

## Methods of Analysis:

There are many different types of method of frame analysis, that’s been below-

**Flexibility Coefficient Method.****Approximate Methods.****Vertical Load.****Horizontal Load.****Substitute Frame Method.****Portal Method.****Cantilever Method.**

**Iterative Methods.****Moment Distribution Method.****Kaniās Method.**

**Slope Displacement Method.**

**#1. ****Flexibility Coefficient Method-**

**Coefficients** of the unknowns in equations to be solved are “**flexibility**” **coefficients**. Force (**Flexibility**) **Method** For determinate structures, the force **method** allows us to find internal forces (using equilibrium i.e. based on Statics) irrespective of the material information.

The flexibility coefficient method is also known as the force method or compatibility method. The flexibility coefficient method is considering the geometrical condition imposed on the formation of structures. This method is mainly used for analysing frames of low D.O.R.

**#2. Approximate Methods**–

For the preliminary design of the frame, the approximate analysis of the hyperstatic structure provides a simple means of obtaining a quick solution.

To obtain a rapid solution of a complex structure, the approximate method makes use of simplifying assumptions regarding structural behavior. The location of zero moments in the structure each point of inflection corresponds.

**The approximate method is carried out separately for these two case-**

**Vertical Loads-****Horizontal Loads-**

**#2.1. Vertical Loads-**

- On the beam and column, the stress and the structure subjected to a vertical load depend upon the relative stiffness.
- The approximate method either assumes adopts simplified moment distributed methods or an adequate number of hinges to render the structure determinate.

**#2.2. Horizontal Loads-**

To depends on its height to width ratio, the structure is subjected to a horizontal force. It is dominated by bending action in a high-rise building where the height is several times greater than its lateral dimensions. The structure subjected to horizontal loading there is three methods are analysis.

**Substitute Frame Method.****Portal Method.****Cantilever Method.**

**#2.2.1. Portal Method-**

**Portal**frame can be defined as two-dimensional rigid frames that have the basic characteristics of a rigid joint between column and beam.**Portal**frame construction is a**method**of building and designing structures- The method makes simplifying assumption regarding horizontal shear in columns in low-rise structure. In the portal method, the point of inflection occurs at the mid-point of the beams.

**#2.2.2. Cantilever Method- **

- The
**cantilever method**is very similar to the portal**method**. We still put hinges at the middles of the beams and columns. - The only difference is that for the
**cantilever method**, instead of finding the shears in the columns first using an assumption, we will find the axial force in the columns using an assumption. - For the high-rise building structure, this method is applicable. On the axial force of columns, this method is based on simplifying assumptions.

**#2.2.3. Substitute Frame Method-**

**Substitute frame method**assumes that the moments in the beams of any floor are influenced by loading on that floor alone.- The influence of loading on the lower or upper floors is ignored altogether. The process involves the division of multi-storied structure into smaller
**frames**. - The substitute frame method assumes that the moment in the beams of any floor is influenced by loading on that floor alone.
- The multi-storeyed structure into the smaller frame the division process is involved. The subframes are known as substitute frames.

**#3. Iterative Methods-**

- Indeterminate structure, the iterative method is a powerful method of frame analysis. The iterative method is simple and adequate for the usual structure of frame analysis.
- The distribution of the joint moments this method based on the among members connected to the joint.

There are a few sub-methods of iterative method thatās are below-

**Moment Distribution Method.****Kaniās Method.**

**#3.1. Moment Distribution Method-**

- The
**moment distribution method**is a structural analysis**method**for statically indeterminate beams and frames developed by Hardy Cross. - In the moment distribution method, the structural system is at first reduced to its kinematically determinate. This is accomplished by assuming all joints to be fully restrained.
- For this condition of the structure, the fixed end moment is calculated. By releasing them successively, the joint is allowed to deflect rotate.
- It was published in 1930 in an ASCE journal. The
**method**only accounts for flexural effects and ignores axial and shear effects.

**#3.2. Kaniās Method-**

**Kani’s method**was introduced by Gasper**Kani**in 1940’s. 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.- Kani’s
**method**is also known as the Rotation contribution**method**. - In order to satisfy the condition of continuity of slope and displacement, it involves distributing the unknown fixed end moments of structural members to the adjacent point. Kaniās method distributed the total joint moment at any stage of iteration.

**#4. Slope Displacement Method-**

- The
**slope deflection method**is a structural analysis**method**for beams and frames introduced in 1914 by George A. Maney. - The
**slope deflection method**was widely used for more than a decade until the moment distribution**method**was developed. - The slope displacement method is also called stiffness or displacement or equilibrium method. It is expressing the relation between the moments acting at the ends of the members is consist of a series of the simultaneous equation that is written in term of slope deflection.
- We gate the value of unknown rotation of the joints by a solution of slope deflection equation along with the equilibrium equation. The end moment is calculated slope deflection equation by knowing this rotation.

## Structural Frame Analysis-

Structural frame analysis determines the effects of loads on the structural components and the physical structure. This type of analysis includes all that must withstand loads, such as buildings, bridges, aircraft, and ships.

The result of structural frame analysis is used to verify a structure’s fitness for use, often precluding physical tests. In the engineering design of structures, the structural frame analysis is a key part.

## Approximate Method of Structural Analysis-

**Approximate analysis** is conducted by making realistic assumptions about the behavior of the **structure**.

**Approximate Analysis** of Indeterminate Trusses During preliminary design and **analysis**, the actual member dimensions are not usually known. Note the areas of cross-sections of the columns are different.

The approximate method of structural analysis is useful for determining the moment and forces in the different members of the frame or structure. By making a realistic assumption about the behavior of the structure, the approximate method of structural analysis is conduct.

The approximate method of structural analysis has below submethods-

**Portal Method.****Cantilever Method.**

**#1. Portal Method-**

- In the portal method, the point of inflection occurs at the mid-point of the beams.
- The method makes simplifying assumption regarding horizontal shear in columns in low-rise structure.

**#2. Cantilever Method-**

- On the axial force of columns, this method is based on simplifying assumptions.
- For the high-rise building structure, this method is applicable.

## Method of Consistent Deformation-

The force **method** (also called the flexibility **method** or **method of consistent deformation** ) is used to calculate reactions and internal forces in statically indeterminate structures due to loads and imposed **deformations**. The system thus formed is called the basic determinate structure.

The method of consistent deformation is also called the flexibility method or force method. Method of consistent deformation is used to calculate the reactions and forces of statically indeterminate structures.

Method of consistent deformation is useful for statically indeterminate structures of the single-story building and uncommon geometry building.

Method of consistent deformation is a process where the structure is transformed into a statically determinate system, and then we calculate all the system of forces by applying the boundary condition.

**Frame Analysis Example:**

Before constructing a building, you need to do frame analysis. B frame analysis method, we can easily determine each and every structural condition of that building. Examples of frame analysis are done by mainly four methods, those four methods are-

**Flexibility Coefficient Method.****Slope Displacement Method.****Iterative Method.****Approximate Method.**

Mainly by these methods, the frame analysis is done.

**Slope Deflection Method Frame:**

The slope deflection method is a method that consists of structural analysis of beams and frames. In the slope deflection method, the frame consists of a simultaneous equation expressed the moments acted at the end of the member.

In the slope deflection method of frames, rotation of angles is measured with slope deflection equation and joint & shear equilibrium conditions. The slope deflection method frame process is only effective in structures with small kinematic indeterminacy.

**Force Method Structural Analysis:**

Force method structural analysis is also called the flexibility method or method of consistent deformation.

Force method structural analysis is a process where the structure is transformed into a statically determinate system, and then we calculate all the system of forces by applying the boundary condition.

Force method structural analysis is useful for statically indeterminate structures of the single-story building and uncommon geometry building. Force method structural analysis is used to calculate the reactions and forces of statically indeterminate structures.

## Analysis of Statically Indeterminate Structures by the Force Method:

**Force** (Flexibility) **Method** For **determinate structures**, the **force method** allows us to find internal **forces** (using equilibrium i.e. based on Statics) irrespective of the material information.

However, for **indeterminate structures**, Statics (equilibrium) alone is not sufficient to conduct **structural analysis**.

Analysis of statically indeterminate structure by force method is a process where the structure is transformed into a statically determinate system, and then we calculate all the system of forces by applying the boundary condition.

Here statically indeterminate structures of the single-story building and uncommon geometry building are analysed by force method. The analysis by the force method is used to calculate the reactions and forces of statically indeterminate structures.

**Moment Distribution Method Frame:**

In the **moment distribution method**, initially, the structure is rigidly fixed at every joint or support. The fixed end **moments** are calculated for any loading under consideration.

Subsequently, one joint at a time is then released. When the **moment** is released at the joint, the joint **moment** becomes unbalanced.

The moment distribution method of the frame is generally suitable for statically indeterminate structures. In the moment distribution method, we consider all the joints are fully restrained.

Here the joints are allowed to rotate one by one after releasing them. The moment distribution method frame analysis method is appropriate for analysing continuous beam, including a non-prismatic beam.

By the use of the moment distribution method, to obtain the Fixed Moment of the unsymmetrical frame, we need to analyse it more than once. The moment distribution method frame is also applicable for intermediate hinge structures.

## Portal Frame Analysis:

In the portal frame analysis method, we consider horizontal shear in columns. Here every structure is considered as a portal frame, and the horizontal force is distributed equally. Portal frame analysis method, we observed that the inflection point is situated at the mid-height of every column.

In frame analysis, in the mid-span of the beam, the inflection points occur. In the portal frame analysis method, the loads are distributed to all the columns, so the outer columns carry the half forces and the rest of the forces carried by inner columns.

**Force Method for Beams:**

The force method for beams is also called the flexibility method or method of consistent deformation. The force method of beams is used to calculate the reactions and forces of statically indeterminate structures.

Force method of beams is useful for statically indeterminate structures of the single-story building and uncommon geometry building.

The force method of beams is a process where the structure is transformed into a statically determinate system, and then we calculate all the system of forces by applying the boundary condition.

## FAQ: Analysis Methods for Building Frames

### What Are the Primary Methods for Analyzing Building Frames?

**Building Frames Analyze by Approximate Methods for Vertical Loads****Building Frames Analyse by the Cantilever Method for Horizontal Loads****Building Frame Analyses by the Portal Method for Horizontal Loads**

### What Assumptions Are Made in the Approximate Methods for Vertical Loads?

- Zero moments occur at the support of the beam.
- The frame analysis is considered as a fixed beam subjected to vertical loads.

### How Does the Cantilever Method Address Horizontal Loads?

- The building frame is designed to withstand lateral loads, such as those from earthquakes.
- The actual deflection of the beam is considered, typically showing the deflection as dotted lines.

### What Are the Key Assumptions in the Portal Method for Horizontal Loads?

- Inflection points occur at the mid-height of each column.
- Interior columns carry twice the shear of exterior columns, dividing the total horizontal shear between the columns of each story.

### What Is the Flexibility Coefficient Method?

- Also known as the force method or compatibility method, it uses flexibility coefficients to solve for internal forces irrespective of material information.
- It is mainly used for analyzing frames with low degrees of redundancy.

### How Is the Approximate Method Used for Vertical and Horizontal Loads?

- For vertical loads, stress and structure depend on relative stiffness, often using simplified moment distribution methods.
- For horizontal loads, methods such as the Substitute Frame Method, Portal Method, and Cantilever Method are used based on the structure’s height to width ratio.

### What Is the Substitute Frame Method?

- It assumes that moments in the beams of any floor are influenced only by loading on that floor, ignoring the influence of loads on other floors.
- This involves dividing a multi-story structure into smaller frames, known as substitute frames.

### How Do Iterative Methods, Such as the Moment Distribution Method, Work?

- They involve distributing the joint moments among members connected to the joint.
- The Moment Distribution Method reduces the structure to its kinematically determinate form, calculates fixed end moments, and releases joints successively to allow deflection and rotation.

### What Is Kaniās Method?

- Introduced by Gasper Kani, it distributes unknown fixed end moments to adjacent joints to satisfy continuity of slopes and displacements.
- Also known as the Rotation Contribution Method.

### What Is the Slope Displacement Method?

- Introduced by George A. Maney, this method uses a series of simultaneous equations expressing moments at the ends of members in terms of slope deflection.
- It calculates unknown rotations of joints and determines end moments accordingly.

### What Is the Importance of Structural Frame Analysis?

- It determines the effects of loads on structural components and the overall structure, verifying the structure’s fitness for use without physical tests.
- It is crucial in the engineering design of buildings, bridges, aircraft, and ships.

### How Is the Approximate Method Useful in Structural Analysis?

- By making realistic assumptions about structural behavior, it simplifies the determination of moments and forces in frame members.
- Useful for preliminary design and analysis when actual member dimensions are not known.

### What Are the Key Features of the Portal Frame Analysis?

- Inflection points occur at the mid-height of columns and mid-span of beams.
- Horizontal shear in columns is considered, with loads distributed such that outer columns carry half the forces of inner columns.

### How Does the Force Method for Beams Work?

- Also known as the flexibility method, it transforms the structure into a statically determinate system to calculate forces by applying boundary conditions.
- Suitable for statically indeterminate structures of single-story buildings and those with uncommon geometry.