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**What Is Structural Analysis?**

**Structural analysis **is the method of determining and calculating the effects of loads and internal forces acting on a structure, building, or object. It is a process determining the response of the structure to specified arbitrary external loads.

**Structural Analysis **of structure is essential before starting construction work. It provides the details of the size of the foundation, the size of the column and beam, and reinforcement details that are sufficient to carry the load acting on the structure. Before constructing any structure, there are several documents required like plan, elevation & section details.

This process of finding out the load that a structure can carry safely, without failure is called **Structure Analysis.**

**Understand the Word â€˜Structureâ€™**

The most general definition of a structure is a building or an object made from several parts. From an engineering point of view, the structure may be defined as follows:

**The structure** is composed of a number of components or **elements connected together **by joints or supports to fulfill the function for which it is constructed; in such a way that they can **transmit the forces** coming on the structure to the foundation **safely** without showing **considerable deformation**.

**Structural Analysis Basic Concepts**

The** concept of structural analysis** is applied not only in building constructions but also in our day-to-day life.

**For instance,**

- The aluminum container for carrying food parcels is provided with vertical ribs, which can impart stiffness to it. As a result, it becomes easier to carry it without bending.
- The game of building blocks, which you might have played in childhood, is also based on principles of structural analysis. If you insert several blocks in a straight line, then the blocks will fall.

A similar phenomenon happens in the case of the buildings. Slender buildings that are very tall tend to collapse.

However, you can prevent this by providing a firm base, i.e., increasing the fixidity at the base.

**Importance of Structural Analysis**

- To know the behavior of the structure under the loaded condition.
- To know the maximum load up to which the structure can be loaded, so that the structure will not fail.
- To ensure that the displacement and deformation remain in the permissible limits.

**Structural Elements**

As discussed earlier, a structure is composed of many parts joined together to transfer the loads. These parts are referred to as elements/members in structural analysis. Some of the structural elements are mentioned below:

**Beam**: A horizontal member transmitting transverse loads. Resists loads applied laterally to the beam axis. The load produces shear and bending moment in the beam.

**Column**: A vertical member carrying only gravity loads. It transmits axial force or bending force.

**Truss**: A structure having slender members connected by pin-joint. It carries axial load only, applied at joints. Members undergo either compression or tension.

**Grid**: Network of beams intersecting each other at right angles. Vertical loading is transmitted through grids.

**Frame**: Network of beams and columns with rigid joints.

**Plates**: Members carrying bending in two directions are called plate structures.

Continuum mechanics principles are followed in their analysis. Concrete flat slab is an example of a plate structure

**Arch**: Members carrying compression in one direction only.

**Types of Load Act on Structure**

Following are the load act on structure,

### 1. **Dead Loads**

The loads on the structure due to the self-weight of the building and the weight of the permanent furniture are classified as dead loads.

To calculate dead load,

- Assess the quantity of the material
- Multiply it by the unit weight of the material

**Dead Load = Quantity of Material x Unit Weight**

The unit weights of the material can be found out from IS: 875(Part I)- 1987.

### 2. **Imposed Loads**

The loads that are â€˜imposedâ€™ on the structure are called imposed load. The following loads are included I imposed loads:

### 3. **Live Load**:

The loads which change their position with respect to time are called live loads.

E.g., weight of a person, furniture, moving partitions, etc.

The minimum values to be taken for the design purpose are given in IS:875 (Part II)- 1987 based on the occupancy of the building, i.e., whether the structure is residential, warehouse, etc.

### 4. **Crane load**:

Loads from the crane and other moving machinery is called crane load.

These loads are vital for the structure. If they are not considered, then the structure may undergo failure during its erection itself!

These loads can be known from the manufacturerâ€™s data.

### 5. **Wave Load**

For off-shore structures, these loads are essential.

e.g., force exerted by water current to the bridge piers, abutments, and other waterfront structures

These are random loads, and specialists with enough experience are needed to determine them.

### 6. **Earth Pressure Load**

The pressure exerted by the soil on the structures or part of structure embedded partly or fully in the ground is called earth pressure.

These loads are required for the foundation of the structures.

These are also needed for the design of retaining walls, underground water tanks, culverts, bridges, etc.

### 7. **Impact Load**

The structures carrying moving loads are to be designed for impact loads.

e.g., bridge

### 8. **Wind Loads**

The force exerted on the structures by the horizontal component of the wind is considered under the wind load.

It is considered for the design of tall buildings.

### 9. **Earthquake Loads**

the earthquake causes shaking of ground in all directions, and role reversal in the structural elements take place.

As the ground shakes horizontally, horizontal inertia forces are generated. These lateral forces are transferred through slabs, beams, and columns.

And Columns that are designed to carry compressive loads start getting tensile loads too.

So, the lateral forces are evaluated to make the structure earthquake-resistant.

**What data is needed for Structural Analysis?**

The following values are needed to be for executing any structural analysis,

- Material properties (To know the value of Elastic Modulus)
- Structural load
- Support conditions
- Geometry

**What do we find after Structural Analysis?**

As you complete the Structural analysis, you will have the values of:

- Support reactions
- Displacement value
- Stress in the member

These values are then compared to the criteria for structural failure to conclude how much load the member will be able to resist.

**Classification of Structures**

**Based on Type,**

- Solid structure
- Frame structure
- Membrane structure
- Composite structure

**Based on Form**,

- 1-D structures: Rope, cable. Strut, beam, column, and arch
- 2-D structures: slab, membranes, domes, and plates
- 3-D structures: Solid masses

**Based on Determinacy of the structure**,

**Determinate structure**: The structure whose support reactions and internal forces in the members can be found out from the*equations of static equilibrium*is called a statically determinate structure.

2. **Indeterminate structures**: The structure whose support reactions and internal forces in the members can NOT be found out from the *equations of static equilibrium* is called a statically indeterminate structure.

Indeterminate structures are further classified into **statically** or **kinematically** indeterminate structures.

**Equations of Static Equilibrium**

The structure should remain in equilibrium after a load is applied to it. In simple terms, no component of the structure should exhibit motion on the application of load. When can this condition be fulfilled?

If the structure possesses sufficient rigidity to develop reactions in response to the loads applied on it, then the equilibrium of the structure is achieved.

To check whether a structure will be in equilibrium or not, three mathematical equations are developed for two-dimensional structures, and six mathematical equations are developed for three-dimensional structures.

**For 2-D Structures,**

The following 3 conditions should be fulfilled:

- The summation of the forces in the horizontal direction should be zero.
- The summation of the forces in the vertical direction should be zero.
- The summation of the moments about the direction perpendicular to both the above forces should be zero.

**For 3-D Structures**,

The following 6 conditions should be fulfilled:

- The summation of the forces in the horizontal direction (
**X**) should be zero - The summation of the forces in the vertical direction(
**Y**) should be zero - The summation of the forces in the direction perpendicular to both horizontal and vertical directions (
) should be zero*Z* - The summation of the moments in the horizontal direction(
**X**) should be zero - The summation of the moments in the vertical direction(
**Y**) should be zero - The summation of the moments about the direction perpendicular to both horizontal and vertical directions (
) forces should be zero*Z*

**Basic Concept of Structural Analysis**

The structural analysis can be completed by applying the following step-by-step procedure:

**1. Idealization of Structure**

For structural analysis, idealization of the structural system is done to simplify the structure and making the calculations simpler and easier.

Some of the idealizations that we are aware are listed below:

- We assume the beam as a line structure.
- The joints of a truss are pin-jointed.
- In truss, we assume loads are acting only on joints; the loads acting on members cause bending moments, which is not suitable for the truss. And as we have assumed truss to possess pin or hinge joints, it cannot take bending moments.

**2. Threats on Structures**

The threats on structures are the forces acting on it, which tends to reduce its capacity and stability. These can be in the form of various loads, as discussed earlier.

- Concentrated load
- Distributed load
- Concentrated moment
- Distributed moment

**3. Calculating the response of Structure under the Threat:**

- Internal force (axial, shear or moment)
- Defection

**4. Calculation of Internal Stresses**

Internal stresses include:

**Bending stresses**: Caused by the*bending*moment.**Shear stresses**: Caused by the*shear*force.

## Efficiency of the Structure

**Efficiency**: The structural efficiency is the measure of the mass of a structure to the load it can support safely without excessive deformation and deflections.

If a structure is lighter and supports heavy loads, then its efficiency is deemed higher.

**Analysis of Determinate Structures**

The following methods may be implemented for the analysis of the Determinate Structures,

For Beams,

- Macaulayâ€™s method
- Moment area method
- Conjugate beam method
- Consistent Deformation method
- From Influence Line Diagrams

**6. For Plane Truss and Frame**

- Method of Joints
- Method of Sections
- Unit load method
- From Influence Line Diagrams

**7. Analysis of Indeterminate Structures**

Compatibility equations and Principle of Superposition are mostly applied during the analysis of indeterminate structures.

The following methods may be implemented for the analysis of the Indeterminate Structures

**8. For Beams, Plane Truss and Frame**

- Castiglianoâ€™s Theorem
- Slope Deflection method
- Moment Distribution method
- From Influence Line Diagrams
*(Used for structures having Moving Loads, like Bridges)* - Matrix methods
- Stiffness method

- Flexibility method

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