Shear Force And Bending Moment

What Is a Beam?

A beam is a structural element that carries loads mainly by bending. Beams are commonly used in:

• Buildings (floors and roofs)
• Bridges
• Frames and platforms
• Machines and supports

When loads act on a beam, internal forces develop inside it. The two most critical internal effects are shear force and bending moment.

What Is Shear Force?

Shear force is the internal force that acts perpendicular to the length of a beam.

Simple Definition

Shear force tries to slide one part of the beam over another.

Example

Imagine cutting a beam at a certain point. The force that tries to push the two cut sections apart sideways is the shear force at that point.

Key Points About Shear Force

• It varies along the length of the beam
• It depends on the type of load and supports
• Maximum shear usually occurs near supports
• It is measured in kN (kilonewtons)

What Is Bending Moment?

Bending moment is the internal moment that causes the beam to bend or curve under load.

Simple Definition

Bending moment tries to bend the beam into a curved shape.

Example

When you place a load at the center of a beam, the beam sags. The force causing this sagging is the bending moment.

Key Points About Bending Moment

• It varies along the beam length
• Maximum bending moment often occurs at mid-span or fixed supports
• It is measured in kN·m
• It controls beam strength and design size

Relationship Between Load, Shear Force, and Bending Moment

These three are closely connected:

• Loads create shear forces
• Shear forces create bending moments
• Bending moments cause deflection

In simple terms:

Load → Shear Force → Bending Moment → Deflection

This is why engineers always study shear force and bending moment together.

Types of Beams Commonly Used

Your calculator supports two common beam types, which are also the most important in practice.

1. Simply Supported Beam

• Supported at both ends
• Free to rotate
• No moment at supports

Common Uses

• Floor beams
• Bridge spans
• Roof supports

2. Cantilever Beam

• Fixed at one end
• Free at the other end
• High bending moment at the fixed support

Common Uses

• Balconies
• Canopies
• Overhanging slabs

Types of Loads Acting on Beams

Different loads create different shear force and bending moment patterns.

1. Point Load

A load acting at a single point.

Examples

• Column load on a beam
• Heavy machine placed at one spot

Behavior

• Sudden jump in shear force
• Linear change in bending moment

2. Uniformly Distributed Load (UDL)

A load spread evenly along the beam.

Examples

• Self-weight of beam
• Floor load

Behavior

• Shear force changes linearly
• Bending moment forms a smooth curve
• Maximum bending moment at mid-span (for simply supported beams)

3. Triangular Distributed Load

Load intensity varies from zero to maximum.

Examples

• Earth pressure
• Wind pressure
• Water pressure

Behavior

• Shear force curve
• Bending moment curve with shifted maximum location

Shear Force Diagram (SFD)

A shear force diagram shows how shear force changes along the length of the beam.

Why It Is Important

• Identifies maximum shear force
• Helps in checking shear failure
• Guides reinforcement design in RCC beams

Key Observations

• Sudden vertical jumps indicate point loads
• Sloping lines indicate distributed loads
• Maximum shear usually occurs at supports

Bending Moment Diagram (BMD)

A bending moment diagram shows how bending moment varies along the beam.

Why It Is Important

• Identifies maximum bending moment
• Helps determine beam depth and size
• Controls structural safety and stiffness

Key Observations

• Zero moment at simple supports
• Maximum moment at mid-span (UDL on simply supported beam)
• Maximum moment at fixed support for cantilever beams

Maximum Shear Force and Maximum Bending Moment

Engineers always focus on maximum values because failure usually starts there.

Maximum Shear Force

• Used to check shear strength
• Important for web reinforcement design

Maximum Bending Moment

• Used to design beam size
• Controls tension and compression zones

Your calculator directly provides:

• Maximum shear force
• Maximum bending moment
• Location of maximum moment

This saves time and reduces manual calculation errors.

Beam Deflection and Its Importance

Deflection is how much a beam bends under load.

Why Deflection Matters

• Excessive deflection causes cracks
• Affects appearance and comfort
• Can damage finishes and partitions

Factors Affecting Deflection

• Load magnitude
• Beam length
• Young’s Modulus (E)
• Moment of inertia (I)

The calculator estimates maximum deflection assuming:

• Linear elastic behavior
• Small deformations

Role of Material Properties

Young’s Modulus (E)

• Measures material stiffness
• Higher E = less deflection
• Steel has higher E than concrete

Moment of Inertia (I)

• Depends on beam shape
• Larger I = stronger resistance to bending
• Depth of beam has major impact on I

Why Use a Shear Force and Bending Moment Calculator?

Manual calculations are useful for learning, but in practice they can be:

• Time-consuming
• Error-prone
• Hard to repeat for multiple cases

A calculator helps you:

• Quickly analyze different beam types
• Compare load conditions
• Identify critical values instantly
• Improve design accuracy

Engineering Assumptions to Remember

Most shear force and bending moment calculations assume:

• Linear elastic material behavior
• Small deflections
• Ideal supports
• Static loading

For real projects, always follow:

• Design codes
• Safety factors
• Professional judgment

Real-World Importance of Shear Force and Bending Moment

Understanding these concepts helps prevent:

• Beam cracking
• Excessive sagging
• Sudden structural failure
• Unsafe building design

Every safe structure starts with proper shear force and bending moment analysis.