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A weld is used for joining an angle section $\text{ISA}$ $100 \:mm \times 100\:mm \times 10 \:mm$ to a gusset plate of thickness $15$ $\text{mm}$ to transmit a tensile load. The permissible stress in the angle is $150$ $\text{MPa}$ and the permissible shear stress on the section through the throat of the fillet weld is $108$ $\text{MPa}$. The location of the centroid of the angle is represented by $C_{yy}$ in the figure, where $C_{yy} = 28.4$ $\text{mm}$. The area of cross-section of the angle is $1903\: mm^{2}$. Assuming the effective throat thickness of the weld to be $0.7$ times the given weld size, the lengths $L_{1}$ and $L_{2}$ (rounded off to the nearest integer) of the weld required to transmit a load equal to the full strength of the tension member are, respectively.

  1. $541$ $\text{mm}$ and $214$ $\text{mm}$
  2. $214$ $\text{mm}$ and $541$ $\text{mm}$
  3. $380$ $\text{mm}$ and $151$ $\text{mm}$
  4. $151$ $\text{mm}$ and $380$ $\text{mm}$
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