Mastering Shear Force and Bending Moment Diagrams

The stress-strain curve graphically represents how a structure responds to loads. Stress-strain curves are an accurate method of demonstrating the mechanical properties of a structure such as modulus of elasticity, limit of proportionality, yield stress, proof stress, and more. Understanding stress-strain curves is a fundamental requirement needed to advance in this course. 

This week will cover

• Concepts of stress and strain
• Important aspects of stress-strain curves of steel and concrete materials
• Hooke’s law
• Modulus of elasticity
• Limit of proportionality
• Yield stress
• Proof stress
• Fundamentals of equilibrium state 
• Types of equilibrium
• Equilibrium equations
• Beams and their various types

A single-span beam is only supported at the ends, and can be analyzed under various loading conditions. The applied load can be constant or vary with time. It is important for learners to understand the approach used to analyse single-span beams and their behaviour under loading conditions. 

This week will cover

• Analysis approach for single-span beams
• Types of loading
• Uniform loading
• Concentrated load
• Linearly varying load
• Determining the bending moment and shear force diagrams of beams
• Sign convention used in the industry

A structure is said to be statically indeterminate when the equilibrium equations alone are not enough for calculating the forces. Such statically indeterminate structures can be analysed using two methods, stiffness method and force method. It is important to understand the concepts of indeterminacy in structures and equilibrium equations to advance in this field.

This week will cover

• Statically indeterminate beams
• Different methods of analysis of statically indeterminate structures 
• Stiffness method
• Force method
• Equilibrium and deformation compatibility equations 
• Overview on Castigliano’s theorem for determining displacements
• Determination of bending moment and shear force diagrams of a single span statically indeterminate beam
• Analysis of propped cantilever beam subjected to uniform load and concentrated load

A beam that has more than two supports is called a continuous beam. A continuous beam that consists of two single-span beams connected to each other by internal hinges is known as a two-span continuous beam. Unwanted moment forces can be avoided by using hinges. It is important for learners to understand how two span continuous beams with internal hinges are analyzed. 

This week will cover

• Internal hinges in statically indeterminate beams along with real-life examples
• Implications of internal hinges on bending moments
• Analysis of single-span and two-span beams with internal hinge
• Determining bending moment and shear force diagrams

Influence line diagrams help determine the site of loading for a particular structure by capturing the applied load. Most often, a structure is subjected to concentrated moving loads. Concentrated loads are applied at a specific point. If the point of application varies with time, it is called concentrated moving load. It is important to understand the concepts involved in influence line diagrams and moving loads. 

This week will cover

• Concept of influence line diagram and its applications
• Influence lines of vertical reactions for a single span simply supported beam
• Concept of moving loads
• Determining absolute maximum bending moment in a beam due to a system of concentrated loads

Müller-Breslau’s principle is a widely used method for drawing influence line diagrams of structures. An influence line diagram for a determinate structure is a straight lin, and for an indeterminate structure, it is a curve. It is important to understand the concepts involved in Müller-Breslau’s principle, as well as its applications.

This week will cover

• Müller-Breslau’s principle 
• Concept of load patterning
• Application of Müller-Breslau’s principle 
• Determination of qualitatively maximum moment in midspan
• Maximum moment over support
• Maximum support reaction for multi-span beams

Flexible supports in beams are provided to reduce the frictional forces in them. Springs are one of the most commonly used flexible supports.These have a number of applications particularly in the case of statically indeterminate structures. It is important to understand the use of flexible supports in continuous beams.

This week will cover

• Concept of flexible supports
• Real-life examples of flexible supports
• Importance of considering support’s flexibility in statically indeterminate beams
• Analysis of two-span beam with one of the supports as spring
• Significance of support flexibility by comparing the analytical findings to a two-span beam without flexible supports.

Portal frames are low-rise structures in which vertical supports and horizontal beams are connected using fixed joints. A portal structure is a wide-span, weather proof structure that can be constructed within a shorter span of time. It is important for learners to understand the construction of various types of portal frame structures. 

This week will cover

• Portal frame structures
• Various types of portal frames 
• Single storey single bay
• Single storey two bays
• Two storeys single bay
• Two storeys two bays
• Multi-storied multibay 
• Application of portal frames in real-life structures like steel and concrete buildings

The structural integrity of a single-storey portal frame construction under gravity loads can be verified using the moment distribution and slope deflection methods. Moment distribution method is used for uniform loads while the slope deflection method is used for concentrated loads. It is important to understand the concepts involved in these two methods.

This week will cover

• Analysis of single-storey portal frame with fixed base subjected to concentrated load using slope deflection method
• The concept of the sway of the portal frame due to gravity loads

Single-storey portal frame structures are widely used for workshops, factories and warehouses. These structures are analyzed for structural integrity by subjecting them to lateral loading conditions. It is important to understand the different methods used for analyzing such portal frame structures.

This week will cover

• Analysis of single-storey portal frame with fixed bases using slope deflection method

A multi-storey steel portal frame is subjected to analysis under various loading conditions. Approximate analysis of multi-storey portal frame structures can be using two methods. They are the portal frame method and cantilever method. It is important to understand the approximate methods used for analyzing multi-storey portal frames. 

This week will cover

• Approximate methods of analysis of multi-storied portal frames using
• Portal frame method
• Cantilever method
• Derivation of bending moment and shear force diagrams

ETABS is a design and analysis software that is most widely used for multi-storey buildings. It can efficiently perform modeling, analysis, design and reporting of building structures.This tool can be used for modeling a wide range of structures from simple 2D frames to complex high-rise buildings. It is essential for learners to understand how to work with ETABS software in order to model structures as needed. 

This week will cover

• Overview of the ETABS software
• Demonstration of ETABS analysis of single and multi-span beams.
• Modeling flexible support in ETABS is demonstrated.
• Demonstration of ETABS's analysis of single-story and multi-story portal frames under varied support situations.
• Measuring sway deformation and lateral drifts in the portal frame.