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BENDING MOMENTS AND SHEAR FORCES

FOR STATICALLY DETERMINATE STRUCTURES

STRUCTURAL ANALYSIS AND DESIGN UNIT - 01

Introduction

If a structure can be solved by equations of statics alone, it is said to be statically

determinate

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Structure is an assemblage of a number of

components like slabs, beams, columns,

walls, foundations and so on, which remains

in equilibrium

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BEAMS

Beams - usually long, straight members designed to support loads applied at various points along the member

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Beams

Columns

Members that are slender and support loads applied perpendicular to their longitudinal axis

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BEAMS

Span, L

Distributed Load, w(x) Concentrated Load, P

Longitudinal Axis

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Slab Beam

Beam

Beam

Beam

Columns

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Types of Beams

Cantilever Beam

Simply Supported Beam

Overhanging Beam

Continuous Beam

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Concentrated or Point Load

Uniformly Distributed Load

Uniformly Varying Load

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Types of Loading

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Types of Loads

Dead Load

Live Load

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Dead Load Self weigh of beams, columns,

walls, trusses etc

Live Load Forces of nature, snow load,

associated with intended use of area

Types of Supports

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Types of Support Conditions

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Free body diagram

A sketch of a structural component with all the appropriate forces acting on it

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Beam Analysis - Assumptions

Material of beam is homogenous and isotropic

Plane sections remain plane

Beam is initially straight and all longitudinal filaments bend in circular arcs

Neutral Axis is Located at Centroid

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Axial Force

Algebraic sum of all forces acting parallel to the longitudinal axis of the member on either side of the section

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Positive Axial Force Negative Axial Force

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Shear Force

Shear force at any section is the algebraic sum of all forces either to the left or right of the section

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The shear force tends to rotate the material clockwise is defined as positive

Positive Shear Negative Shear

Bending Moment

Bending moment at any cross section is the algebraic sum of moments of all forces either to the left or right of the section

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