Question

The two plates are welded by a butt joint and is subjected to tensile force P as shown in figure. The average tensile stress in the weld is

• A. $\sigma_t = 2P / (hl)$
• B. $\sigma_t = P / (2hl)$
• C. $\sigma_t = P / (hl)$
• D. $\sigma_t = 2P / (3hl)$

Hint:

For a butt weld, the throat thickness is simply the thickness of the thinner plate ($h$). Thus, the stress area is straightforwardly $h \times l$.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question is about calculating the average tensile stress in a butt-welded joint under a tensile load $P$.

Step 2: Key Formula or Approach:
The average normal stress ($\sigma$) on any section is defined as the applied load divided by the cross-sectional area resisting that load:
\[ \sigma_t = \frac{\text{Force } (P)}{\text{Resisting Area } (A)} \]

Step 3: Detailed Explanation:

• A butt joint is designed to join two plates such that their surfaces are in the same plane.

• When subjected to a tensile force $P$, the cross-sectional area of the weld that resists this tension is the throat area.

• The throat thickness is equal to the plate thickness $h$, and the length of the weld is $l$.

• Therefore, the area resisting the tensile load is:
\[ A = h \cdot l \]

• Substituting this area into the stress formula gives:
\[ \sigma_t = \frac{P}{h \cdot l} \]

Step 4: Final Answer:
The average tensile stress in the weld is $\sigma_t = \frac{P}{hl}$.