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Overview

End length offsets, also known as rigid arms or rigid zones, allow you to model rigid end zones at member connections. This is essential for accurately representing the behavior of members connected to large joints or when accounting for the actual width of connections in a structure. In real structures, connections often have finite dimensions. For example, when a beam frames into a wide column, the beam doesn’t actually connect at a single point but extends into the column. End length offsets account for this behavior by creating rigid zones at member ends.

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When to Use End Offsets

Beam-Column Connections

Account for column width when beams frame into wide columns

Rigid Joints

Model joints with significant dimensions that behave rigidly

Panel Zones

Represent rigid panel zones in moment-resisting frames

Connection Details

Accurately model connection geometry in detailed analyses

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Syntax

model.add_end_length_offset(
    member_id,
    la=0,      # Length offset at start node
    lb=0,      # Length offset at end node
    qla=True,  # Apply loads on start rigid arm
    qlb=True,  # Apply loads on end rigid arm
    fla=1,     # Start rigid zone factor
    flb=1      # End rigid zone factor
)

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Parameters

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member_id
int
required
ID of the member to apply the end offset to
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la
float
default:"0"
Length offset at the start node (node i). Positive values extend the rigid zone away from the member.
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lb
float
default:"0"
Length offset at the end node (node j). Positive values extend the rigid zone away from the member.
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qla
bool
default:"True"
Whether to apply loads on the start rigid arm. If True, loads applied to the start node affect the rigid arm.
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qlb
bool
default:"True"
Whether to apply loads on the end rigid arm. If True, loads applied to the end node affect the rigid arm.
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fla
float
default:"1"
Stiffness factor for the start rigid zone (typically 1 for fully rigid)
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flb
float
default:"1"
Stiffness factor for the end rigid zone (typically 1 for fully rigid)

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Examples

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Beam Framing into Column

When a beam frames into a column, you can offset the beam connection to account for the column width: 
from milcapy import SystemModel, BeamTheoriesType

model = SystemModel()

# Define material and sections
model.add_material("steel", modulus_elasticity=2.1e8, poisson_ratio=0.3)
model.add_rectangular_section("column", "steel", base=0.4, height=0.4)
model.add_rectangular_section("beam", "steel", base=0.3, height=0.5)

# Create column (vertical member)
model.add_node(1, 0, 0)
model.add_node(2, 0, 3)
model.add_member(1, 1, 2, "column", BeamTheoriesType.TIMOSHENKO)

# Create beam (horizontal member)
model.add_node(3, 5, 3)
model.add_member(2, 2, 3, "beam", BeamTheoriesType.TIMOSHENKO)

# Apply end offset to account for column width (0.4m / 2 = 0.2m)
column_width = 0.4
length_offset = column_width / 2

model.add_end_length_offset(
    member_id=2,
    la=length_offset,  # Offset at connection to column
    qla=True           # Apply loads on rigid arm
)

# Add restraints
model.add_restraint(1, True, True, True)
model.add_restraint(3, False, True, False)

# Add loads
model.add_load_pattern("Dead Load")
model.add_point_load(3, "Dead Load", fx=0, fy=-50, mz=0)

# Solve and visualize
model.solve()
model.show()
The end offset is typically half the width of the connecting member to represent the rigid zone extending from the centerline to the face of the member.

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Symmetric Connection with Both End Offsets

For a beam connected to columns on both ends: 
# Create model with columns on both ends
model.add_node(1, 0, 3)     # Left column top
model.add_node(2, 5, 3)     # Right column top
model.add_node(3, 10, 3)    # Far right column top

# Beam spanning between columns
model.add_member(5, 1, 3, "beam", BeamTheoriesType.TIMOSHENKO)

# Apply offsets on both ends
length_offset = 0.2  # Half of column width

model.add_end_length_offset(
    member_id=5,
    la=length_offset,  # Offset at left column
    lb=length_offset,  # Offset at right column
    qla=True,
    qlb=True
)

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Advanced: Variable Rigid Zone Factors

You can adjust the stiffness of the rigid zones using the fla and flb parameters: 
# Create semi-rigid end zones (50% stiffness)
model.add_end_length_offset(
    member_id=3,
    la=0.15,
    lb=0.15,
    fla=0.5,  # 50% rigid at start
    flb=0.5   # 50% rigid at end
)
Changing the rigid zone factors from 1.0 creates semi-rigid connections, which may not be appropriate for all analyses. Use fla=1 and flb=1 for fully rigid end zones in most cases.

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Load Application on Rigid Arms

The qla and qlb parameters control whether loads applied to the nodes are transferred to the rigid arms:
  • qla=True / qlb=True: Loads on the node are applied to the rigid arm (typical case)
  • qla=False / qlb=False: Loads on the node bypass the rigid arm and go directly to the flexible member
# Loads applied to rigid arm (typical)
model.add_end_length_offset(2, la=0.2, qla=True)

# Loads bypass rigid arm (special case)
model.add_end_length_offset(3, la=0.2, qla=False)

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Effect on Analysis Results

End length offsets affect:
  1. Member forces: The effective length of the flexible portion is reduced
  2. Displacements: Rigid zones don’t deform, affecting overall displacement patterns
  3. Moment distribution: Moments are transferred through the rigid zones
  4. Effective stiffness: The model’s overall stiffness changes due to the rigid connections
Always verify that your end offsets correctly represent the physical geometry of your structure. Incorrect offsets can lead to significant errors in analysis results.

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Best Practices

  1. Use realistic dimensions: Base offsets on actual member dimensions
  2. Check geometry: Verify that rigid zones don’t overlap or create invalid geometry
  3. Document assumptions: Keep track of which members have offsets and why
  4. Validate results: Compare results with and without offsets to understand their impact

Member Releases

Control moment and force transfer at connections

Elastic Supports

Add spring supports to nodes

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