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structuralwith-tool

Composite Section

Calculates transformed section properties for a simplified steel I-girder with concrete slab and haunch using the modular ratio method. The template reports transformed area, neutral axis, second moment of area, and top and bottom section moduli.

with-tool: The model is given an executable Python calculator script.

Standards

AASHTO LRFD 6.10 AS/NZS 5100.6

Tags

bridge composite-section deterministic section-properties structural

How this task is generated

One template produces many comparable benchmark tasks while keeping the scoring contract fixed.

01
Template
The reusable contract shown on this page.
02
Scenario
An archetype and site context are sampled.
03
Difficulty tier
Inputs may be hidden at harder tiers.
04
Task prompt
The model responds with the declared outputs.

Parameters

Inputs the model receives, and the outputs it is scored on.

Inputs

11 inputs

Always given

Included directly in every task prompt.

11

Show 11 inputs

Top flange width
top_flange_width_mm
Steel top flange width
50 – 2000 mm
Top flange thickness
top_flange_thickness_mm
Steel top flange thickness
5 – 150 mm
Web depth
web_depth_mm
Clear steel web depth between flanges
100 – 5000 mm
Web thickness
web_thickness_mm
Steel web thickness
5 – 100 mm
Bottom flange width
bottom_flange_width_mm
Steel bottom flange width
50 – 2000 mm
Bottom flange thickness
bottom_flange_thickness_mm
Steel bottom flange thickness
5 – 150 mm
Slab width
slab_width_mm
Effective concrete slab width
100 – 10000 mm
Slab thickness
slab_thickness_mm
Concrete slab thickness
50 – 500 mm
Haunch width
haunch_width_mm
Concrete haunch width
50 – 3000 mm
Haunch thickness
haunch_thickness_mm
Concrete haunch thickness
10 – 500 mm
Modular ratio
modular_ratio
Steel-to-concrete modular ratio
1 – 20

Scored outputs

5 outputs

Transformed area

transformed_area_mm2

Transformed composite section area

Scores if within ±3% of the reference value.

Neutral axis from bottom

neutral_axis_from_bottom_mm

Neutral axis from bottom of steel section

Scores if within ±3% of the reference value.

Transformed inertia mm4

transformed_inertia_mm4

Transformed second moment of area

Scores if within ±3% of the reference value.

Bottom section modulus mm3

bottom_section_modulus_mm3

Bottom section modulus

Scores if within ±3% of the reference value.

Top section modulus mm3

top_section_modulus_mm3

Top section modulus

Scores if within ±3% of the reference value.

Difficulty

Each template is sampled at three tiers. Harder tiers may hide inputs, forcing the model to infer them from the scenario description.

All inputs remain visible at every tier

For this template, difficulty scales through parameter and scenario ranges rather than hidden information.

easy:: All parameters given for a rolled girder
medium:: All parameters given across composite girder types
hard:: All parameters given for a bridge plate girder

Task bundle

The exact instruction and parameter contract used to generate this task, pinned to the published library source.

/workspace

instruction.md
composite-section_calc.py

Teal lines show Jinja input conditions, not task visibility policy. A line renders only when that input or tool is visible.

1You are a senior structural engineer specializing in bridge composite section design.2 3## Task4 5Calculate transformed section properties for the steel-concrete composite girder in {{ site_context }}.6 7## Given8 9| Parameter | Value | Unit |10| --- | ---: | --- |11| Top flange width | {{ top_flange_width_mm }} | mm |12| Top flange thickness | {{ top_flange_thickness_mm }} | mm |13| Web depth between flanges | {{ web_depth_mm }} | mm |14| Web thickness | {{ web_thickness_mm }} | mm |15| Bottom flange width | {{ bottom_flange_width_mm }} | mm |16| Bottom flange thickness | {{ bottom_flange_thickness_mm }} | mm |17| Effective slab width | {{ slab_width_mm }} | mm |18| Slab thickness | {{ slab_thickness_mm }} | mm |19| Haunch width | {{ haunch_width_mm }} | mm |20| Haunch thickness | {{ haunch_thickness_mm }} | mm |21| Modular ratio | {{ modular_ratio }} | - |22 23## Constraints24 25- No internet access is available.26- Use transformed-section analysis with concrete area and inertia divided by the modular ratio.27- Measure vertical dimensions from the bottom of the bottom flange.28- Model the steel section as three rectangles: bottom flange, web, and top flange.29- Model the concrete as two transformed rectangles: haunch and slab.30- Use the parallel-axis theorem to calculate transformed second moment of area.31 32{% if tool_available %}33## Available Tool34 35A calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:36 37```bash38python3 /workspace/{{ meta.name }}_calc.py --help39```40 41You may use this tool to verify your calculations or compute values directly.42{% endif %}43 44## Required45 46Calculate:47 48- Transformed composite section area (`transformed_area_mm2`)49- Neutral axis from bottom of steel section (`neutral_axis_from_bottom_mm`)50- Transformed second moment of area (`transformed_inertia_mm4`)51- Bottom section modulus (`bottom_section_modulus_mm3`)52- Top section modulus (`top_section_modulus_mm3`)53 54## Output Format55 56Show your step-by-step working in Markdown. At the end of your solution, include a JSON block with your final answers in exactly this format:57 58```json59{60  "transformed_area_mm2": <numeric_value>,61  "neutral_axis_from_bottom_mm": <numeric_value>,62  "transformed_inertia_mm4": <numeric_value>,63  "bottom_section_modulus_mm3": <numeric_value>,64  "top_section_modulus_mm3": <numeric_value>65}66```67 68Write your complete solution to `/workspace/output.md`.69

Scenario archetypes

Each generated task is drawn from one of these realistic scenario bands.

Site contexts ground each scenario in a real locale the model can use to infer hidden values.

Plate girder

plate_girder

Bridge plate-girder composite section

bridge-plate-girdercomposite-road-bridge

Parameter ranges

top_flange_width_mm: 300 – 700
top_flange_thickness_mm: 20 – 60
web_depth_mm: 900 – 2500
web_thickness_mm: 10 – 30
bottom_flange_width_mm: 400 – 900
bottom_flange_thickness_mm: 25 – 80
slab_width_mm: 2000 – 5000
slab_thickness_mm: 180 – 300
haunch_width_mm: 300 – 800
haunch_thickness_mm: 50 – 200
modular_ratio: 6 – 12

Rolled girder

rolled_girder

Rolled-girder composite section

rolled-girder-bridgeshort-span-composite-deck

Parameter ranges

top_flange_width_mm: 150 – 350
top_flange_thickness_mm: 10 – 35
web_depth_mm: 400 – 1000
web_thickness_mm: 8 – 20
bottom_flange_width_mm: 150 – 350
bottom_flange_thickness_mm: 10 – 40
slab_width_mm: 1000 – 3000
slab_thickness_mm: 150 – 250
haunch_width_mm: 150 – 500
haunch_thickness_mm: 40 – 150
modular_ratio: 6 – 12

Example task

bridge-plate-girder-plate-girder-preview — hard difficulty, all inputs given.

Bridge plate-girder composite section. bridge-plate-girder. Required outputs: transformed_area_mm2, neutral_axis_from_bottom_mm, transformed_inertia_mm4, bottom_section_modulus_mm3, top_section_modulus_mm3

The model sees

Scenario context and visible inputs.

top_flange_width_mm: 300 to 700 mm
top_flange_thickness_mm: 20 to 60 mm
web_depth_mm: 900 to 2500 mm
web_thickness_mm: 10 to 30 mm
bottom_flange_width_mm: 400 to 900 mm
bottom_flange_thickness_mm: 25 to 80 mm
slab_width_mm: 2000 to 5000 mm
slab_thickness_mm: 180 to 300 mm
haunch_width_mm: 300 to 800 mm
haunch_thickness_mm: 50 to 200 mm
modular_ratio: 6 to 12

Executable tool: composite-section_calc.py

The model must infer

Inputs withheld at this difficulty.

Nothing. All inputs are supplied.

The model must produce

The scored JSON answer schema.

{
  "transformed_area_mm2": <number>,
  "neutral_axis_from_bottom_mm": <number>,
  "transformed_inertia_mm4": <number>,
  "bottom_section_modulus_mm3": <number>,
  "top_section_modulus_mm3": <number>
}

transformed_area_mm2 · scored within ±3%
neutral_axis_from_bottom_mm · scored within ±3%
transformed_inertia_mm4 · scored within ±3%
bottom_section_modulus_mm3 · scored within ±3%
top_section_modulus_mm3 · scored within ±3%