Truss Analysis & Design Glossary
Key terminology for modern structural analysis and design.
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A
Assembly Process
The procedure of combining the individual Member Stiffness Matrices into the single, large Global Stiffness Matrix by summing contributions at the corresponding Degrees of Freedom.
Axial Force
The internal force acting along the longitudinal axis of a truss member. It is either tension (positive axial force, pulling the member apart) or compression (negative axial force, pushing the member together).
B
Boundary Conditions
The constraints on the structure's motion imposed by its supports. These typically define specific Degrees of Freedom where displacement is zero (e.g., \( D_x = 0 \) or \( D_y = 0 \)).
Buckling
A mode of failure in slender compression members where the member suddenly bends laterally due to instability, occurring at a load lower than the material's yield strength.
C
Common Truss Shapes
Standard truss geometries, such as the Pratt, Warren, Howe, and Fink trusses, often used for roofs and bridges due to their efficiency.
Compression Member
A truss member subjected to a pushing force (negative axial force) that tends to shorten it. These members must be checked for buckling.
Cross-sectional Area \( A \)
The area of the member perpendicular to its longitudinal axis. This property, along with Young's Modulus and Length, determines a member's stiffness \( AE/L \).
Custom Truss Geometry
Any truss configuration designed specifically for a unique application, not conforming to a standard, named shape.
D
Dead Load
The constant, gravity-driven load of a structure, including the weight of the structure itself and any permanent fixtures (e.g., decking, roofing, ceiling).
Degree of Freedom (DOF)
An independent way a node can move. In a 2D planar truss, each node has two DOFs: horizontal displacement (\( D_x \)) and vertical displacement (\( D_y \)).
Design Dashboard
A centralized screen or interface in structural software where users can input parameters, view key results, and control the analysis process.
Direct Stiffness Method
A systematic, matrix-based method for structural analysis (also known as the Matrix Stiffness Method or Displacement Method). It relates external forces (Load Vector) to nodal displacements (Displacement Vector) via the Global Stiffness Matrix.
Direction Cosines \( (c, s) \)
The cosine \( (c = \cos(\theta)) \) and sine \( (s = \sin(\theta)) \) of the Orientation Angle. They are used extensively to define the member's contribution to the Global Stiffness Matrix.
Displacement Vector \( (\mathbf{D}) \)
A column matrix containing the unknown displacements for every Degree of Freedom in the structure. \( \mathbf{D}_{\mathbf{R}} \) is the Reduced Displacement Vector of unknown displacements to be solved.
Distributed Load
A force acting over a length or area of a structural element, measured in force per unit length (e.g., \( \text{kN/m} \) or \( \text{lb/ft} \)).
F
Factor of Safety
A design ratio used to ensure a structure's capacity exceeds the required load, calculated as the ratio of the ultimate (failure) stress/load to the allowable (working) stress/load.
Finite Element Analysis (FEA)
A powerful numerical method used for solving complex structural problems. The Direct Stiffness Method is the foundational theory for FEA software when analyzing frame and truss structures.
G
Global Coordinate System
The single, overall coordinate system (typically \( \mathbf{x} \) and \( \mathbf{y} \)) used to define the coordinates, forces, and displacements for the entire truss structure.
I
Inversion \( (\mathbf{K}_{\mathbf{R}}^{-1}) \)
The mathematical process of finding the inverse of the Reduced Stiffness Matrix \( (\mathbf{K}_{\mathbf{R}}) \) to solve for unknown displacements: \( \mathbf{D}_{\mathbf{R}} = \mathbf{K}_{\mathbf{R}}^{-1} \cdot \mathbf{Q}_{\mathbf{R}} \).
L
Length \( (L) \)
The distance between the two end nodes of a member, calculated using the coordinates of the start and end nodes.
Linear Elastic Behavior
The assumption that the truss material obeys Hooke's Law \( (\sigma = E\epsilon) \), meaning the relationship between stress and strain is linear and the material will return to its original shape upon removal of the load.
Linear Load Distribution
The application of a load that is spread uniformly or non-uniformly across the length of a member. Software converts this into equivalent nodal forces for truss analysis.
Live Load
A variable load applied to a structure, typically due to occupancy, equipment, or movable objects.
Load Case
A specific combination of applied external forces (loads) and support conditions that a structure must be designed to withstand. Analyzing multiple load cases ensures safety under various real-world scenarios.
Load Vector \( (\mathbf{Q}) \)
A column matrix containing the known external forces applied at every Degree of Freedom of the structure.
Local Coordinate System
The coordinate system used to define forces and displacements along a single member's axis (axial direction) and perpendicular to it.
M
Member
An individual straight component of a truss structure. In ideal truss analysis, members are assumed to carry only Axial Forces.
N
Nodal Load
An external force (sometimes called a Concentrated Load) that acts directly on a truss node. Truss analysis assumes all external forces are applied this way.
Node (Joint)
The connection point where two or more truss members meet. It is assumed to be a frictionless pin connection that cannot transfer moments.
O
Optimized Member Design
A process where the system automatically selects the most efficient member cross-section that can safely carry the calculated axial forces without failure.
Orientation Angle \( (\theta) \)
The angle a member makes with the positive \( \mathbf{x} \)-axis, measured counterclockwise. It is critical for transforming member properties from local to global coordinates.
P
Planar Truss
A truss structure where all members and applied loads lie within a single two-dimensional plane (x-y plane).
R
Reduced Stiffness Matrix \( (\mathbf{K}_{\mathbf{R}}) \)
The smaller matrix formed by removing the rows and columns of the Global Stiffness Matrix that correspond to the known, zero-displacement Degrees of Freedom (Boundary Conditions).
S
Small Deformations
The assumption that displacements are small enough that the initial geometry of the truss is considered unchanged throughout the analysis, simplifying the force-displacement relationships.
Snow Load
The load applied to a roof structure by accumulated snow and ice, a type of gravity load that is typically variable.
Static Equilibrium Check
The essential step to verify the final results by confirming that the sum of all forces (applied loads + support reactions) and moments equals zero.
Statically Determinate
A truss structure whose internal forces and support reactions can be entirely determined using only the equations of static equilibrium \( (\Sigma F_x = 0, \Sigma F_y = 0, \Sigma M = 0) \).
Statically Indeterminate
A truss structure with more supports or members than required for static stability. Its analysis requires considering material properties and member deformations.
Steel HSS
Hollow Structural Section, a type of structural steel member with a hollow, typically square, rectangular, or circular cross-section.
Stiffness Equation
The fundamental matrix equation of the method: \( \mathbf{Q} = \mathbf{K} \cdot \mathbf{D} \).
Stiffness Matrix \( (\mathbf{k} \text{ or } \mathbf{K}) \)
A matrix that relates forces and displacements. \( \mathbf{k}_i \) is the Member Stiffness Matrix; \( \mathbf{K} \) is the Global Stiffness Matrix for the entire structure.
Strain \( (\epsilon) \)
The measure of deformation in a material, calculated as the change in length \( (\Delta L) \) divided by the original length \( (L) \).
Stress \( (\sigma) \)
The internal force intensity within a material, calculated as the axial force \( (P) \) divided by the cross-sectional area \( (A) \). \( \sigma = P/A \).
Submittal-Ready Report
Professional documentation generated by analysis software that includes key inputs, calculation steps, and final results suitable for submission to regulatory authorities or clients.
Support Reaction
An external force or moment exerted by a support (like a pin or roller) on the truss to maintain static equilibrium against applied loads.
T
Tension Member
A truss member subjected to a pulling force (positive axial force) that tends to lengthen it. These members are checked for yielding or fracture.
Timber
Structural lumber used for construction. Member design involves selecting an appropriate grade and dimension.
Truss
A structural system composed of straight members connected at their ends by pin joints (nodes). It is designed to transfer forces primarily through axial loading (tension or compression).
W
Wind Load
Forces exerted by wind pressure or suction on the exterior surfaces of a structure. This is often an important load case for tall or exposed trusses.
Y
Yielding
The point at which a material begins to deform permanently (plastically) under stress. For tension members, the yield strength is a critical design limit.
Young's Modulus \( (E) \)
A measure of the stiffness of an elastic material; the ratio of stress to strain in the linear elastic range (Hooke's Law). Also called the Elastic Modulus.