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Question
Consider the following statments related to axial and eccentric loading in vertical members and choose the correct option. 
Statements:
(1)   For solid rectangular vertical members, the core is a rhombus of diamond shape.
(2)   For vertical members subjected to eccentric compressive force, for no tension in the section the eccentricity (e) should be less than 2d2/K (Where d = depth of section and k = radius of  gyration)
A.
Statement 2 is true and statement 1 is false
B.
Statement 1 is true and statement 2 is false
C.
Both statements are false.
D.
Both statements are true
Answer ( Option B)

Statement 1 is true and statement 2 is false

Solution

For a rectangular section of width b and depth d:

To ensure that no tensile stress is produced in the section,

Where,

· e = eccentricity of the load

· k = radius of gyration of the section

· y  = distance from the centroid to the extreme fibre

For a rectangular section,
Where k is the radius of gyration of the section.

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