Module 7 · Lesson 7.3
Offsets and eccentricity
The rigid arm between a node and the member it actually connects to, and the moment it carries.
Why this matters
Analysis models are drawn on centrelines. Structures are not. A beam frames into a column face, a slab sits on top of a beam rather than through its middle, a brace works to a gusset rather than to the intersection of two centrelines.
The distance between the two is the offset, and the model handles it with a rigid arm. That arm carries the shear across the eccentricity and turns it into a moment — one whose size is exactly predictable, and which is simply absent from the centreline model.
By the end of this lesson you should be able to
- Say what a rigid offset represents physically
- Compute the moment an offset introduces
- Explain why offsets change the clear span as well as the moments
- Decide when an offset is worth modelling
The rigid arm
An offset is a rigid connection between the node and the physical end of the member. It has two effects, and both are easy to overlook:
It shortens the member. The structural span is now between the offset ends, not between the nodes. A 6 m beam framing 250 mm into a column has a clear span of 5.75 m and is stiffer accordingly.
It carries force across a distance. The member's end shear reaches the node through the arm, and a force applied at a distance is a moment.
Exactly V·e
A beam framing into a column face at eccentricity e, carrying end shear V: the column receives the beam's end moment plus V·e. Not approximately — exactly, and it comes straight out of statics on the rigid arm.
For a 6 m beam at 20 kN/m into a 4 m column:
| Eccentricity | Clear span | Beam end moment | Column top moment | Difference |
|---|---|---|---|---|
| 0 | 6.00 m | 59.68 kN·m | 59.68 kN·m | 0 |
| 0.10 m | 5.90 m | 54.71 | 61.53 | 6.83 |
| 0.20 m | 5.80 m | 49.81 | 63.13 | 13.32 |
| 0.30 m | 5.70 m | 44.99 | 64.46 | 19.47 |
At e = 0 the two moments are identical, as they must be — with no arm there is nothing to carry a moment across. At e = 0.30 m the difference is 19.47 kN·m, and the end shear at that eccentricity is 64.89 kN: 64.89 × 0.30 = 19.47. Exactly.
Read the two moment columns together and the effect is clear: the beam's end moment falls and the column's rises. The centreline model reports the beam moment for both, so it under-predicts the column by the whole of V·e.
When it is worth modelling
Offsets add work and add places to make mistakes, so they should not be added everywhere. Three cases where they earn it:
Deep members into shallow ones. A 900 mm transfer beam into a 400 mm column has an eccentricity comparable with the member depth, and V·e is not a correction.
Bracing to gussets. A brace working to a gusset rather than to the theoretical work point puts moment into the connection that the centreline model has nowhere to show.
Composite floors. The slab's centroid sits above the beam's, which is the entire mechanism of composite action. Modelling it with an offset rather than a transformed section makes the eccentricity explicit.
And one case where it usually does not: ordinary beam-to-column connections in a regular frame. The eccentricity is small compared with the member sizes and the effect is within the other uncertainties. Recording that as a decision — in the exclusions field of the purpose statement — is better than either modelling it everywhere or forgetting it exists.
What it calculates: The moment a supporting member receives when the beam frames into its face rather than its centreline
- V
- beam end shear (kN)
- e
- eccentricity from the node to the physical member end (m)
- M
- moment (kN·m)
This assumes
- The offset is modelled as a rigid arm, with no flexibility of its own
In plain terms: The relation is exact and comes from statics on the arm. A centreline model has e = 0, so it reports the beam's end moment for the column too, and under-predicts by the whole of V·e.
Try it
Offset and eccentricity explorer
A beam framing into a column face rather than its centreline. Watch the clear span, the two moments, and what the rigid arm carries.
- Clear span
- 5.750 m
- Beam end moment
- 47.39 kN·m
- Column top moment
- 63.83 kN·m
- Beam end shear
- 65.74 kN
- Carried by the rigid arm
- 16.44 kN·m
- Centreline model reports, for both
- 59.68 kN·m
- Column under-predicted by
- 7.0 %
grid span 6 m
V × e = 65.74 × 0.250
The beam's end moment falls and the column's rises. The difference between them is exactly the end shear times the eccentricity, and the centreline model has no mechanism by which it could show it.
What this shows: The arm carries the end shear across the eccentricity: exactly V·e, and a centreline model contains none of it.
Practice
A beam frames into a column face at an eccentricity of 0.25 m and its end shear is 80 kN. What moment does the rigid arm add to the column?
Practice
A 6 m beam frames 0.30 m into columns at both ends. What is its clear span?
Summary
- An offset is a rigid arm between the node and the physical member end
- It shortens the clear span, which stiffens the member
- It carries the end shear across the eccentricity: exactly V·e
- The beam's end moment falls and the supporting member's rises
- A centreline model under-predicts the column by the whole of V·e
- Worth modelling for deep-into-shallow, bracing to gussets, and composite floors
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint