Bolt group eccentric shear calculator
Four bolts on a 3 by 3 square with 1000 pushing down 3 units from the centroid: the worst bolt takes 500 downward plus 250 sideways, while the direct share is only 250. You see every bolt's resultant and which one governs. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Force x
- 0
- Force y
- -1,000
- Load x
- 4.5
- Load y
- 1.5
- Bolt count
- 4
- Centroid x
- 1.5
- Centroid y
- 1.5
- Eccentricity x
- 3
When a bracket or gusset carries an in-plane force that does not pass through the centroid of a bolt pattern, every fastener sees a combination of shared direct shear and additional rotational shear from the eccentricity moment. Students, connection detailers, and early-stage steel checkers need that critical resultant without building a full finite-element model or re-deriving polar second moments by hand for every geometry. This bolt group eccentric shear calculator accepts bolt coordinates, force components, and the load application point, computes the equal-area centroid and polar second moment J, superposes direct shear P over n with elastic rotational components M r over J, and reports the most heavily loaded fastener together with per-bolt resultants.
What eccentric bolt-group shear means and how elastic vector analysis works
A bolt group under an in-plane load that misses the pattern centroid develops a moment about that centroid equal to the force times its eccentricity. In the classic elastic, or vector, method used throughout structural steel textbooks and many hand-calculation checklists, each equal fastener is assumed to share the applied force equally as direct shear while the moment is resisted by shear forces proportional to each bolt’s distance from the centroid.
Relative positions x-prime and y-prime are measured from that centroid, and the polar second moment J is the sum of x-prime squared plus y-prime squared. The moment M about the centroid is the planar cross product of the load-application vector from the centroid with the force vector. Rotational components on bolt i are Fr_x equals negative M times y-prime over J and Fr_y equals M times x-prime over J, which produces a force magnitude M times r over J perpendicular to the radius vector.
The resultant on each bolt is the vector sum of direct and rotational parts; the critical fastener is the one with the largest resultant magnitude. Search intent for this landing clusters around bolt group eccentric shear calculator, elastic vector method critical bolt, eccentric load bolt pattern shear, and fastener group eccentric force analysis. People want a numeric critical shear they can compare to a textbook key or a spreadsheet, not only a reminder that eccentricity creates moment.
Practical use, limits, pricing, and when to step up to code methods
Use the browser tool when you want an immediate elastic critical-bolt check while grading eccentric connection homework, verifying a hand calculation for a bracket with an offset load, teaching how rotational shear grows with distance from the centroid, or comparing a rectangular pattern before opening a detailed connection model. Results are fully deterministic: identical inputs always produce the same centroid, moment, J, per-bolt resultants, and critical index.
There is no language model, no external structural analysis service, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible course materials. When your problem requires AISC ultimate strength with the instantaneous center of rotation, combined tension and shear interaction, prying action, or plate yielding, switch to a code-compliant connection design tool; this calculator stays focused on elastic vector shear so the answer stays transparent and fast.
What you can do with it
Homework and exam elastic vector checks
Students and graders enter bolt coordinates, force components, and load point to obtain the critical resultant and per-bolt shears for comparison with textbook elastic method solutions.
Preliminary eccentric bracket sizing
Detailers and makers estimate the most loaded fastener in a planar pattern before running full code-compliant connection design or finite-element checks.
FAQ
How does this bolt group eccentric shear calculator work?
It finds the equal-area centroid, forms moment M of the force about that centroid, shares direct shear as P/n, adds rotational shear components Frx=−M y′/J and Fry=M x′/J, and reports the bolt with the largest resultant magnitude.
What coordinates and units should I use?
The engine does not convert units; resultants are in your force unit.
Is this the same as the ultimate strength (ICR) method?
No. This tool implements the elastic vector method only. Instantaneous-center ultimate strength, interaction equations, and code reductions are out of scope.
Which bolt is critical in an eccentric bolt group?
The bolt with the largest combined force once its direct shear and its twisting share are added together; the twisting share grows with distance from the centroid. In the four-bolt example, the two bolts nearest the load each take 500 downward and 250 sideways.
What happens if all the bolts are at the same point?
The polar moment J becomes zero, so the twisting share of the shear is undefined and no result can be given. Enter at least two bolts at different positions, all in the same length unit.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/eng/bolt-group-eccentric \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"bolts":[{"x":0,"y":0},{"x":3,"y":0},{"x":0,"y":3},{"x":3,"y":3}],"force_x":0,"force_y":-1000,"load_x":4.5,"load_y":1.5}'const res = await fetch("https://api.kit.forhosting.com/eng/bolt-group-eccentric", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"bolts": [
{
"x": 0,
"y": 0
},
{
"x": 3,
"y": 0
},
{
"x": 0,
"y": 3
},
{
"x": 3,
"y": 3
}
],
"force_x": 0,
"force_y": -1000,
"load_x": 4.5,
"load_y": 1.5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/eng/bolt-group-eccentric",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"bolts": [
{
"x": 0,
"y": 0
},
{
"x": 3,
"y": 0
},
{
"x": 0,
"y": 3
},
{
"x": 3,
"y": 3
}
],
"force_x": 0,
"force_y": -1000,
"load_x": 4.5,
"load_y": 1.5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/eng/bolt-group-eccentric", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"bolts":[{"x":0,"y":0},{"x":3,"y":0},{"x":0,"y":3},{"x":3,"y":3}],"force_x":0,"force_y":-1000,"load_x":4.5,"load_y":1.5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"bolts":[{"x":0,"y":0},{"x":3,"y":0},{"x":0,"y":3},{"x":3,"y":3}],"force_x":0,"force_y":-1000,"load_x":4.5,"load_y":1.5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/eng/bolt-group-eccentric", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"bolts": [
{
"x": 0,
"y": 0
},
{
"x": 3,
"y": 0
},
{
"x": 0,
"y": 3
},
{
"x": 3,
"y": 3
}
],
"force_x": 0,
"force_y": -1000,
"load_x": 4.5,
"load_y": 1.5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "eng.bolt_group_eccentric",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
What eccentric bolt-group shear means and how elastic vector analysis works
With n bolts at coordinates (x_i, y_i), the centroid is the arithmetic mean of the coordinates. Direct shear components are force_x over n and force_y over n.
Input contract, units, validation, and response shape
After validation the engine builds the centroid, relative coordinates, polar second moment J, and the moment of the force about the centroid. There is no code-check reduction for bolt holes, no interaction equation with tension, no ultimate-strength instantaneous center of rotation method, and no unit conversion table—this capability is elastic in-plane shear superposition only. Send a JSON body with a required bolts array of at least two {x, y} objects in one consistent length unit, plus four finite numbers: force_x and force_y for the applied force components in a consistent force unit, and load_x and load_y for the coordinates of the force application point in the same length unit as the bolts. Each numeric field may arrive as a JSON number or as a numeric string; missing fields, empty strings, non-numeric text, NaN, and Infinity fail immediately with invalid_input and are not charged. Optional aliases such as fasteners or points for the array, fx and fy for force components, and apply_x or apply_y for the load point are accepted when documented so forms and scripts can use common symbols. If all fasteners coincide so that J is zero, rotational shear is undefined and the request is rejected with an explicit message rather than a division by zero. Successful responses echo inputs and derived geometry, list every bolt with direct, rotational, and resultant components, and identify critical_index (zero-based, first maximum on ties) with critical_resultant magnitude and components. The same pure function powers the free in-browser tool and the API path, with no network, no random seed, and no wall-clock timestamp in the computation path.
Practical use, limits, pricing, and when to step up to code methods
Each successful request is one billable item at $0.002; failed validation does not consume balance. Keep force units consistent for force_x and force_y and length units consistent for bolt coordinates and the load point; the engine does not convert units and reports forces in the same unit you supplied. Wire the endpoint into statics drills, preliminary connection worksheets, catalog demos, or preprocessing steps where you prefer explicit domain errors—such as rejecting a zero polar moment—over opaque widgets that cannot explain why a geometry is unsolvable.
Integration use cases
Deterministic fixtures for connection pipelines
Lesson platforms and unit tests call a pure elastic vector oracle instead of reimplementing centroid, J, and M r/J superposition in every language runtime.
Technical questions
What if all bolts are at the same point?
The request fails with invalid_input because the polar second moment J is zero and rotational shear M r/J is undefined. Provide at least two distinct fastener positions.
What does the bolt group eccentric shear calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.