Question:
Length of plastic hinge of a beam depends on :
A. Span of the beam
B. Type of loading
C. Shape of cross-section
D. Yield strength of steel
Choose the correct answer from the options given below :
Length of plastic hinge of a beam depends on :
A. Span of the beam
B. Type of loading
C. Shape of cross-section
D. Yield strength of steel
Choose the correct answer from the options given below :
A. Span of the beam
B. Type of loading
C. Shape of cross-section
D. Yield strength of steel
Choose the correct answer from the options given below :
Show Hint
The plastic hinge length is the distance over which the moment $M$ stays between $M_y$ and $M_p$. It represents the ductility of the member!
Updated On: May 20, 2026
- A and B only
- A, B and C only
- B and C only
- A and D only
Show Solution
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The Correct Option is B
Solution and Explanation
Concept:
A plastic hinge is a zone in a structural member where plastic rotation occurs at a constant plastic moment ($M_p$). The length of this zone ($L_p$) is where the bending moment exceeds the yield moment ($M_y$).
Step 1: Analyze the influence of loading and span.
The length of the plastic hinge depends on the moment gradient. For a simply supported beam with a central point load, $L_p = L(1 - 1/S)$, where $L$ is the span and $S$ is the shape factor. For a beam with a UDL, the length formula changes. Thus, both the Span (A) and the Type of loading (B) are critical factors.
Step 2: Analyze the influence of section geometry.
As seen in the formula $L_p = L(1 - 1/S)$, the Shape of cross-section (C) determines the shape factor ($S$). A section with a higher shape factor (like a diamond) will have a longer plastic hinge compared to an I-section.
Step 3: Analyze Yield Strength.
The yield strength ($f_y$) affects the magnitude of $M_p$ and $M_y$, but since the shape factor is a ratio ($M_p/M_y$), the yield strength cancels out in the geometric calculation of the length of the hinge. Thus, (D) is not a primary factor.
Step 1: Analyze the influence of loading and span.
The length of the plastic hinge depends on the moment gradient. For a simply supported beam with a central point load, $L_p = L(1 - 1/S)$, where $L$ is the span and $S$ is the shape factor. For a beam with a UDL, the length formula changes. Thus, both the Span (A) and the Type of loading (B) are critical factors.
Step 2: Analyze the influence of section geometry.
As seen in the formula $L_p = L(1 - 1/S)$, the Shape of cross-section (C) determines the shape factor ($S$). A section with a higher shape factor (like a diamond) will have a longer plastic hinge compared to an I-section.
Step 3: Analyze Yield Strength.
The yield strength ($f_y$) affects the magnitude of $M_p$ and $M_y$, but since the shape factor is a ratio ($M_p/M_y$), the yield strength cancels out in the geometric calculation of the length of the hinge. Thus, (D) is not a primary factor.
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