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

Question

If the ratio of the diameter of rivet hole to the pitch of rivets is 0.25, then the efficiency of the circumferential lap joint is:

Answer 1

A parallel fillet weld is loaded along the direction of the weld length, and its failure plane is always the throat, the 45 degree diagonal section through the weld leg. Getting the throat thickness and the number of active weld runs right is what this question tests.

$\sqrt{2}hl\tau_{all}$: correct. Throat thickness is $h/\sqrt{2}$ per weld, two welds (top and bottom) give total throat area $2 \times hl/\sqrt{2} = \sqrt{2}hl$, and the load at allowable stress is $\tau_{all} \times \sqrt{2}hl$.
$hl\tau_{all}$: wrong, this treats the leg size $h$ itself as the throat thickness and skips the $1/\sqrt{2}$ factor from the 45 degree throat plane.
$hl\tau_{all}/\sqrt{2}$: wrong, this uses only one weld's throat area instead of adding both the top and bottom welds shown in the figure.
$hl\tau_{all}/2$: wrong, this divides by 2 instead of multiplying by $\sqrt{2}$, mixing up the throat factor with a plain half factor.

Combining the correct throat thickness with both weld runs gives critical load $\sqrt{2}hl\tau_{all}$, option A.

Answer 2

A parallel fillet weld is loaded along the direction of the weld length, and its failure plane is always the throat, the 45 degree diagonal section through the weld leg. Getting the throat thickness and the number of active weld runs right is what this question tests.

$\sqrt{2}hl\tau_{all}$: correct. Throat thickness is $h/\sqrt{2}$ per weld, two welds (top and bottom) give total throat area $2 \times hl/\sqrt{2} = \sqrt{2}hl$, and the load at allowable stress is $\tau_{all} \times \sqrt{2}hl$.
$hl\tau_{all}$: wrong, this treats the leg size $h$ itself as the throat thickness and skips the $1/\sqrt{2}$ factor from the 45 degree throat plane.
$hl\tau_{all}/\sqrt{2}$: wrong, this uses only one weld's throat area instead of adding both the top and bottom welds shown in the figure.
$hl\tau_{all}/2$: wrong, this divides by 2 instead of multiplying by $\sqrt{2}$, mixing up the throat factor with a plain half factor.

Combining the correct throat thickness with both weld runs gives critical load $\sqrt{2}hl\tau_{all}$, option A.

Show Hint

The Correct Option is A

Solution and Explanation

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