Material Properties and Structural Elements

Yield Strength

• The stress at which a material shows a specific limiting deviation from stress to strain proportionality

Moment of Inertia

• Also known as the second moment of area
• It measures of an object's resistance to bending
• It is based on the object's geometry and distribution of material around an axis

Ductility

• A material's ability to undergo large inelastic deformations without fracturing

Modulus of Elasticity

• The ratio of normal stress to corresponding strain for tensile and compressive stresses
• This is measured below the material's proportional limit

Strength

• The ability of a material to resist stress without failure

Pre-tensioning

• Stressing high strength steel takes place before concrete hardens

Angle Section

• A structural steel member with an L-shaped cross-section
• Used in frames, bracing, and columns

Axial Load

• Load applied along a structural element's axis
• Usually to a column or beam
• Causes tension or compression

Allowable Stress

• The maximum stress a material can withstand safely under working conditions
• Includes a factor of safety

Cantilever

• A structural element fixed at one end
• Extends horizontally without support at the other end

Lateral Load

• A force applied horizontally to a structure
• e.g., wind or seismic forces

Neutral Axis

• The axis within a beam or structural element where strain is zero during bending
• Separates compressed and tensioned areas

Net Section

• The portion of a structural element’s cross-section that resists applied loads
• Does not include any holes or cutouts

Tensile Strength

• The maximum stress a material can withstand under tensile pulling forces before breaking

Truss

• A framework of structural elements designed to support loads
• Usually consists of triangular units connected at their ends

Centroid

• The "balance point" of an object
• It would balance perfectly if made of uniform material

Varignon's Theorem

• The moment of a force about a point equals the sum of the moments of the components of that force about the same point

Dead Load

• Refers to permanent or stationary loads on a structure
• Includes structure's own weight and permanently attached materials
• Constant over time and do not change

Rigid Frame

• A structural framework composed of columns and beams connected with fixed joints

Radius of Gyration

• Distance from the axis of rotation where cross-sectional area can be concentrated
• Without changing the moment of inertia
• Indicates how area is distributed relative to bending or buckling axis

Polar Moment of Inertia

• The sum of moments of inertia of a cross-section about two perpendicular axes
• These axes pass through the centroid of the section (usually x and y axes)

Live Load

• The temporary, dynamic loads that a structure experiences during its usage or occupation

Mohr's Circle

• How to graphically shows representation of the transformation of stress from one set of axes to another
• Shows the relationship between normal stresses and shear stresses

Section Modulus

• The ratio of a beam's moment of inertia to the distance from the neutral axis
• Distance is measured to the furthest point of the section

Toughness

• The ability of a material to absorb energy

Poisson's Ratio

• A material property that describes the deformation behavior of a material
• When subjected to an axial load (tension or compression)

Shear Modulus

• It is a material property, also known as the Modulus of Rigidity
• Describes how a material deforms when subjected to shear stress

W-shape

• Wide Flange Beam

S-shape

• American Standard Beam

HP

• Bearing Pile

M-shape

• Miscellaneous Section or Miscellaneous Shape

C-shape

• Channel Section

L-shape

• Angle Section

WT-shape

• Wide Tee Beam

PL-shape

• Plate Section

Example Centroid Calculation 1

• A plane area with a specific geometry has x = 54.8 mm
• The plane area includes a rectangle with a partial circle removed on top
• See picture on page 41 for more details

Example Centroid Calculation 2

• A plane area with a specific geometry has y = 36.6 mm
• The plane area includes a rectangle with a partial circle removed on top
• See picture on page 42 for more details

Example Centroid Calculation 3

• A plane area with a specific geometry has x = 19.28 in
• Plane area geometry includes a rectangle on the right side with a trapezoid to the left
• See picture on page 43 for more details

Example Centroid Calculation 4

• A plane area with a specific geometry has y = 6.94 in
• Plane area geometry includes a rectangle on the right side with a trapezoid to the left
• See picture on page 44 for more details

Parallel Axis Theorem

• Allows the moment of inertia of a body or section to be calculated about any axis
• Using its moment of inertia about a parallel axis through its centroid
• The Parallel Axis Theorem, is also known as Transfer Formula

Moment of Inertia of a Rectangle Formula

• Moment of inertia has formula b * d^3 / 12.

Moment of Inertia of a Triangle Formula

• Moment of inertia has formula b * h^3 / 36

Example Moment of Inertia of a T-Section Calculation

• Moment of inertia = 136 cm^4