Understanding Solid Plate Strength Per Pitch Length

The question asks for the strength of an unriveted or solid plate per pitch length. Pitch length ($p$) is typically the distance between the centers of adjacent rivets in a row in a riveted joint. However, when considering an unriveted or solid plate, this pitch length is used as a segment length to define the area resisting tension.

Calculating the Area of the Solid Plate Per Pitch Length

For a solid plate without any holes, over a length equal to the pitch ($p$), the full cross-sectional area is available to resist the tensile load. The plate has a thickness ($t$).

The cross-sectional area of the solid plate per pitch length is given by:

\begin{equation*} \text{Area} = \text{Pitch} \times \text{Thickness} = p \times t \end{equation*}

Determining the Strength of the Solid Plate

The strength of the plate in tension is the maximum tensile force it can withstand before failure. This is calculated by multiplying the resisting area by the maximum permissible tensile stress ($\sigma_t$).

\begin{equation*} \text{Strength} = \text{Area} \times \text{Tensile Stress} \end{equation*}

Substituting the area we calculated:

\begin{equation*} \text{Strength of solid plate per pitch length} = (p \times t) \times \sigma_t = pt\sigma_t \end{equation*}

Analyzing the Given Options

• Option 1: $pd\sigma_t$. This involves the diameter $d$, which is relevant for holes in riveted joints, not for a solid plate.
• Option 2: $pt\sigma_t$. This matches our calculation for the strength of a solid plate per pitch length.
• Option 3: $(p - t)d \times \sigma_t$. This involves both $d$ and $(p-t)$, which relates to plate strength between holes in a riveted joint, not a solid plate.
• Option 4: $(p - d)t \times \sigma_t$. This represents the strength of the plate *between* the holes in a riveted joint, considering the reduced area due to the rivet hole diameter $d$. This is not for a solid or unriveted plate.

Therefore, the strength of the unriveted or solid plate per pitch length is $pt\sigma_t$, which corresponds to option 2.