Question:
A rectangular plate is perfectly welded to a gusset plate with parallel fillet weld joints as shown in the figure below. The length of the weld is \(l\) and the fillet weld leg size is \(h\). The allowable shear strength of the weldment is \(\tau_{all}\). A tensile force \(P\) is applied on the plate in a direction parallel to the length of the weld.
Assuming the throat of the weld as the weakest section, the critical load is
A rectangular plate is perfectly welded to a gusset plate with parallel fillet weld joints as shown in the figure below. The length of the weld is \(l\) and the fillet weld leg size is \(h\). The allowable shear strength of the weldment is \(\tau_{all}\). A tensile force \(P\) is applied on the plate in a direction parallel to the length of the weld.
Assuming the throat of the weld as the weakest section, the critical load is
Assuming the throat of the weld as the weakest section, the critical load is
Show Hint
Find the throat thickness of one fillet weld, then add the throat areas of both welds shown in the figure.
Updated On: Jul 27, 2026
- \(\sqrt{2}hl\tau_{all}\)
- \(hl\tau_{all}\)
- \(hl\tau_{all}/\sqrt{2}\)
- \(hl\tau_{all}/2\)
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The Correct Option is A
Solution and Explanation
Step 1: Set up the throat section of a fillet weld.
For a fillet weld with leg size \(h\), the throat is the diagonal weakest plane of the weld cross section, and its thickness is \(t = h\cos 45^{\circ} = \dfrac{h}{\sqrt{2}}\).
Step 2: Find the throat area of one weld run.
Each weld run has length \(l\), so the throat area of one weld is \(A_t = t \times l = \dfrac{hl}{\sqrt{2}}\).
Step 3: Account for both welds carrying the load.
The figure shows two parallel fillet welds, one on top and one on the bottom of the plate, both carrying the load \(P\) together in shear along their throat. Total throat area \(= 2 \times \dfrac{hl}{\sqrt{2}} = \sqrt{2}hl\).
Step 4: Apply the allowable shear strength condition.
At the critical load the shear stress on the throat reaches \(\tau_{all}\), so \(\tau_{all} = \dfrac{P}{\sqrt{2}hl}\), giving \(P = \sqrt{2}hl\tau_{all}\).
Final Answer:
The critical load the joint can carry is \(\sqrt{2}hl\tau_{all}\). \[ \boxed{P_{critical} = \sqrt{2}\,h\,l\,\tau_{all}} \]
For a fillet weld with leg size \(h\), the throat is the diagonal weakest plane of the weld cross section, and its thickness is \(t = h\cos 45^{\circ} = \dfrac{h}{\sqrt{2}}\).
Step 2: Find the throat area of one weld run.
Each weld run has length \(l\), so the throat area of one weld is \(A_t = t \times l = \dfrac{hl}{\sqrt{2}}\).
Step 3: Account for both welds carrying the load.
The figure shows two parallel fillet welds, one on top and one on the bottom of the plate, both carrying the load \(P\) together in shear along their throat. Total throat area \(= 2 \times \dfrac{hl}{\sqrt{2}} = \sqrt{2}hl\).
Step 4: Apply the allowable shear strength condition.
At the critical load the shear stress on the throat reaches \(\tau_{all}\), so \(\tau_{all} = \dfrac{P}{\sqrt{2}hl}\), giving \(P = \sqrt{2}hl\tau_{all}\).
Final Answer:
The critical load the joint can carry is \(\sqrt{2}hl\tau_{all}\). \[ \boxed{P_{critical} = \sqrt{2}\,h\,l\,\tau_{all}} \]
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