Tools › Structures › Joints › Weld Group Stress › Example

Eccentrically loaded fillet-weld group: 50 kN fitting on a channel by the weld-as-line method (Shigley Example 9-1)

ToolWeld Group Stress
SourceBudynas, R. G., and Nisbett, J. K. (2015). Shigley's Mechanical Engineering Design, 10th ed. McGraw-Hill Education, New York. Example 9-1 and Table 9-1 (case 4); Blodgett, O. W. (1966). Design of Welded Structures. James F. Lincoln Arc Welding Foundation, Cleveland, OH.
LevelUndergraduate

Problem

A 50 kN load is carried by a welded fitting into a 200 mm steel channel; each of the two plates is welded to a channel flange by three 6 mm fillet welds in a channel pattern (vertical weld 190 mm along the flange edge, horizontals 56 mm top and bottom), and the 25 kN half-load acts 100 mm outboard of the channel edge. Estimate the maximum shear stress in the weld, treating the welds as lines, and compare it with the E70 code allowable.

Inputs to Enter

  • Configuration case 4 (channel): b = 56 mm, d = 190 mm, leg h = 6 mm; load point (−100, 95, 0) mm, F_y = −25 kN (loaded by default)
  • Electrode E70XX: F_EXX = 482.6 MPa (70 ksi), weld-metal S_y = 393 MPa (57 ksi); design basis AISC code allowable 0.30 F_EXX
Open the Weld Group Stress tool (loaded with this example)

Answers

  • A = 0.707 · 6 · (2 · 56 + 190) = 1,281 mm² (book 1,280); x̄ = 56²/(2 · 56 + 190) = 10.38 mm (book 10.4); J_u = 1.667 × 10⁶ mm³, J = 0.707 · 6 · J_u = 7.071 × 10⁶ mm⁴ (book 7.07 × 10⁶)
  • M = 25 kN · (100 + 10.4) mm = 2,760 N·m; τ′ = V/A = 19.51 MPa (book 19.5); τ″ = M r/J = 41.13 MPa at the free ends (r = 105.4 mm; book 41.0) and 37.30 MPa at the corners on the channel edge (r = 95.57 mm; book 37.3)
  • Vector sum: 43.93 MPa at the two corners on the channel edge (critical), 37.12 MPa at the free ends; with E70, τ_all = 0.30 · 482.6 = 144.8 MPa, load factor 3.30, M.S. = +2.30; allowable force per unit length 614 kN/m; required leg 1.82 mm; S_sy = 0.577 · 393 = 226.8 MPa, factor against yield 5.16

Notes

The book prints the components (A, x̄, r, J, M, τ′, τ″) and leaves the vector addition to the figure; the resultants above are the tool's vector sums of those components, checked by an independent numpy evaluation (test_weld_group.php). The page is in SI because the example is; the USCS radio converts every value.