CELE Strength of Materials — Simple Stresses and StrainsConcept Map

Concept

Normal (Axial) Stress

Sub Concepts

• Tensile stress
• Compressive stress
• Stress formula σ = P/A
• Saint-Venant's Principle

Relationship To Central

Primary stress type; force perpendicular to cross-section

Concept

Shear Stress

Sub Concepts

• Single shear τ = V/A
• Double shear τ = V/2A
• Connector design
• Bolt and rivet analysis

Relationship To Central

Secondary stress type; force parallel to area

Concept

Bearing Stress

Sub Concepts

• Formula σ_b = P/(d·t)
• Projected bearing area
• Hole tear-out
• Plate crushing

Relationship To Central

Contact pressure between bodies

Concept

Strain

Sub Concepts

• Normal strain ε = δ/L
• Shear strain γ
• Axial deformation
• Lateral deformation

Relationship To Central

Deformation measure; fundamental to stress-strain relationship

Concept

Hooke's Law

Sub Concepts

• Axial form σ = Eε
• Shear form τ = Gγ
• Proportional limit
• Elastic limit

Relationship To Central

Linear elastic relationship between stress and strain

Concept

Elastic Constants

Sub Concepts

• Modulus of elasticity E
• Shear modulus G
• Poisson's ratio ν
• Bulk modulus K
• Interrelationships

Relationship To Central

Material properties governing deformation

Concept

Axial Deformation

Sub Concepts

• Formula δ = PL/(AE)
• Composite bar analysis
• Segmented members
• Integration for varying loads

Relationship To Central

Quantitative calculation of member shortening/elongation

Concept

Thermal Effects

Sub Concepts

• Free thermal expansion δ_T = αLΔT
• Thermal stress σ_T = EαΔT
• Restrained members
• Partial restraint gap analysis

Relationship To Central

Temperature-induced stress and deformation

Concept

Statically Indeterminate Members

Sub Concepts

• Equilibrium equations
• Compatibility equations
• Force-deformation substitution
• Double-fixed bar analysis

Relationship To Central

Complex loading requiring compatibility equations

Concept

Stress-Strain Diagram

Sub Concepts

• Proportional limit
• Elastic limit
• Yield point
• Ultimate strength
• Rupture strength

Relationship To Central

Graphical representation of material behavior

Concept

Generalized Hooke's Law

Sub Concepts

• Biaxial stress state
• Triaxial stress state
• Poisson effect in all directions
• Volumetric strain

Relationship To Central

Multi-directional stress-strain relationships

Concept

Design and Safety

Sub Concepts

• Allowable stress
• Factor of safety
• Yield versus ultimate criteria
• NSCP 2015 provisions
• AISC 360 standards

Relationship To Central

Application of stress-strain concepts to safe design

To

Strain

From

Normal Stress

Strength

strong

Relationship

Stress causes strain; related through modulus E via Hooke's Law

To

Shear Strain

From

Shear Stress

Strength

strong

Relationship

Shear stress produces angular distortion; related through shear modulus G

To

Hole Tear-out

From

Bearing Stress

Strength

strong

Relationship

Bearing stress at contact determines hole failure mode in connections

To

Elastic Constants

From

Hooke's Law

Strength

strong

Relationship

Hooke's Law defines the role of E and G; connects through Poisson's ratio

To

Composite Members

From

Axial Deformation

Strength

strong

Relationship

Deformation formula δ = PL/AE applied separately to each material; compatibility equates deformations

To

Restrained Members

From

Thermal Effects

Strength

strong

Relationship

Thermal stress arises only in restrained members; free expansion causes no stress

To

Compatibility Equations

From

Statically Indeterminate

Strength

strong

Relationship

Indeterminate problems solved by adding compatibility constraint to equilibrium

To

Material Behavior

From

Stress-Strain Diagram

Strength

strong

Relationship

Diagram maps stress regions from elastic through plastic to rupture; informs allowable stress selection

To

Generalized Hooke's Law

From

Poisson's Ratio

Strength

strong

Relationship

Poisson's ratio couples strains in perpendicular directions; essential for multi-axial stress

To

Allowable Stress

From

Design and Safety

Strength

strong

Relationship

Factor of safety and allowable stress derived from yield or ultimate strength via stress-strain curve

To

Normal Stress

From

Saint-Venant's Principle

Strength

moderate

Relationship

Principle justifies use of average stress σ = P/A away from load application points

To

Double Shear

From

Single Shear

Strength

moderate

Relationship

Double shear has factor of 2 in denominator; both are variants of τ = V/A

To

Thermal Deformation

From

Axial Deformation

Strength

moderate

Relationship

Both govern total deformation; thermal δ_T = αLΔT added to or subtracted from mechanical δ

To

Axial Rigidity

From

Modulus of Elasticity

Strength

moderate

Relationship

Product AE is axial rigidity; higher AE means less deformation for same load

To

Proportional Limit

From

Elastic Limit

Strength

moderate

Relationship

Proportional limit is typically the lower bound; elastic limit is where permanent set begins

To

Load Sharing

From

Composite Members

Strength

strong

Relationship

Load distributes between materials inversely proportional to their AE products

To

Summation Formula

From

Segmented Bars

Strength

strong

Relationship

Deformation of segments summed: δ_total = Σ(P_i L_i / A_i E_i)

To

Design and Safety

From

NSCP 2015

Strength

strong

Relationship

Philippine code specifies allowable stresses and design factors; governs civil engineering practice

To

Steel Connection Design

From

AISC 360

Strength

strong

Relationship

AISC standards apply to bolt shear and bearing design; used in conjunction with NSCP

To

Concrete Properties

From

ACI 318

Strength

moderate

Relationship

ACI provides concrete modulus and material properties; used in composite concrete-steel analysis