Question
Download Solution PDFConsider a rectangular column cross section of size 4 m × 2 m. Identify the correct statement.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
B (Width) = 4 m
D (Depth) = 2 m
Central Core (Kernel) of a Rectangular Cross-Section:
The central core of a rectangular cross-section forms a rhombus with diagonals given by \(B/3\) and \(D/3\).
Size of the Rhombus:
Diagonal along the width: \(B/3\)= 4/3= 1.33 m
Diagonal along the depth: \(D/3\)= 2/3= 0.66 m
So, the point load must be applied within the rhombus, centered on the section with diagonals of size 1.33 m × 0.66 m, to ensure that no tensile stresses develop in the column cross-section.
Value of Eccentricity (e) for No Tensile Stress:
Eccentricity Along Width: \(e \leq \frac{B}{6} = \frac{4}{6} = 0.66 \, \text{m} \)
Eccentricity Along Depth: \(e \leq \frac{D}{6} = \frac{2}{6} = 0.33 \, \text{m} \)
Summary:
1. The point load must be applied within the central rhombus (1.33 m × 0.66 m) to prevent tensile stress in the column cross-section.
2. The eccentricity \(e\) should not e×ceed 0.66 m along the width and 0.33 m along the depth to ensure no tensile stresses are developed.
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