Roymech engineering encyclopedia

Rectangular Weld Group Stress Calculator




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Use this rectangular weld group stress calculator to estimate weld stresses in a closed rectangular fillet weld group subject to direct shear loads and an in-plane torsional moment about the weld group centroid.

What does this calculator do?

This calculator estimates the maximum resultant shear stress in a closed rectangular weld group. It combines direct shear stress from applied horizontal and vertical loads with torsional shear stress caused by a moment acting about the weld group centroid.

The calculator provides:

  • effective throat thickness
  • total effective weld throat area
  • direct shear stress from Vx and Vy
  • torsional shear stress at the weld group corners
  • maximum resultant weld stress
  • design allowable stress after safety factor
  • utilisation percentage
  • pass/fail result

This calculator is intended for a closed four-sided rectangular weld group. It should not be used for C-shaped, L-shaped or open weld groups.

Engineering note: This calculator is intended for preliminary engineering calculations and educational use. It assumes a closed rectangular weld group and simplified elastic weld group behaviour. Final weld design should be checked against the relevant design standard, weld procedure, loading conditions, fatigue requirements, inspection requirements and safety factors.

How to Use the Calculator

  1. Enter the weld group width, b. This is the horizontal dimension of the rectangular weld group.
  2. Enter the weld group depth, d. This is the vertical dimension of the rectangular weld group.
  3. Enter the fillet weld size, h. This is the nominal fillet weld size used around the rectangular weld group.
  4. Enter the direct shear loads Vx and Vy. Use positive or negative values to represent the direction of the load.
  5. Enter the torsional moment, T. This is the moment acting about the centroid of the weld group. For an eccentric load, T may be calculated as load multiplied by eccentricity.
  6. Enter the allowable weld shear stress and safety factor. The calculator divides the allowable stress by the safety factor to obtain the design allowable stress.
  7. Click calculate. The calculator will estimate the maximum resultant weld stress and utilisation.

Rectangular Weld Group Stress Diagram

Rectangular weld group stress calculator diagram showing weld group width b, depth d, fillet weld size h, shear loads Vx and Vy, torsional moment T and centroid
Closed rectangular weld group showing shear loads, torsional moment and centroid.

Formulae Used

Total weld length:

L = 2(b + d)

Effective throat thickness:

a = 0.707 h

Total throat area:

A = a L

Unit-line polar moment:

J = (b + d)3 / 6

Throat polar moment:

Ja = a J

Direct shear stresses:

τx = Vx / A
τy = Vy / A

Torsional shear components at a point:

τtx = -T y / Ja
τty = T x / Ja

Resultant weld stress:

τr = √((τx + τtx)2 + (τy + τty)2)

Variables

Symbol Description Units
b Weld group width mm
d Weld group depth mm
h Fillet weld size mm
a Effective throat thickness mm
Vx Horizontal shear load N
Vy Vertical shear load N
T Torsional moment about weld group centroid Nmm
A Total effective throat area mm²
J Unit-line polar moment mm³
Ja Throat polar moment mm&sup4;
τr Resultant weld shear stress N/mm²

Calculator Inputs

Results

Enter the weld group dimensions and loads, then click calculate.

Understanding the Results

Result Meaning
Total throat area The effective weld throat area resisting direct shear load.
Direct shear stress The average shear stress caused by Vx and Vy.
Torsional shear stress The additional shear stress caused by moment T acting about the weld group centroid.
Maximum resultant weld stress The largest combined weld stress calculated at the four weld group corners.
Design allowable stress The allowable weld shear stress divided by the selected safety factor.
Utilisation The maximum resultant stress divided by the design allowable stress. A value below 100% passes this simplified check.

Calculator Limitations

This calculator is for a closed rectangular weld group subject to direct shear and an in-plane torsional moment about the weld group centroid. It is a simplified preliminary calculation.

This Calculator Includes This Calculator Does Not Include
Direct shear from Vx and Vy Open C-shaped, L-shaped or parallel-line weld groups
Torsional moment about the centroid Out-of-plane bending moment checks
Corner resultant stress calculation Fatigue, cyclic loading or fracture checks
Utilisation and pass/fail check Parent metal tearing or plate failure checks
Closed rectangular weld group behaviour Code-specific interaction equations or full Eurocode/AISC compliance

Weld Group Stress Calculation Notes

This calculator first calculates the weld group throat area and polar moment. It then calculates direct shear stress from the applied shear loads and torsional shear stress from the applied moment.

The resultant stress is evaluated at the four corners of the rectangular weld group. The largest resultant value is used for the utilisation check.

For weld group properties only, use the Rectangular Weld Group Properties Calculator.

For a simple direct shear fillet weld calculation, use the Fillet Weld Strength & Size Calculator.

For further weld strength formulae and weld group properties, see the RoyMech reference page: Weld Strength Formulae and Weld Group Properties.

Weld Group Stress Calculator FAQ

What does the weld group stress calculator calculate?

It calculates direct shear stress, torsional shear stress and maximum resultant weld stress for a closed rectangular weld group.

Can this calculator be used for eccentric loading?

Yes, if the eccentric load can be converted into a torsional moment about the weld group centroid. The moment can be entered as T in Nmm.

How do I calculate torsional moment from an eccentric load?

For a load acting at an eccentric distance from the weld group centroid, the torsional moment may be estimated as:

T = P e

where P is the applied load and e is the eccentricity from the weld group centroid.

Does this calculator check final code compliance?

No. This calculator is intended for preliminary engineering checks. Final weld design should be checked against the relevant design standard, material properties, weld procedure and inspection requirements.

Can this calculator be used for C-shaped or L-shaped weld groups?

No. This calculator assumes a closed rectangular weld group. Open or irregular weld groups require different centroid and polar moment calculations.