# Compression Member

 Question 1
The critical bending compressive stress in the extreme fibre of a structural steel section is 1000 MPa. It is given that the yield strength of the steel is 250 MPa, width of flange is 250 mm and thickness of flange is 15 mm. As per the provisions of IS:8002007, the non-dimensional slenderness ratio of the steel cross-section is
 A 0.25 B 0.5 C 0.75 D 2
GATE CE 2019 SET-2   Design of Steel Structures
Question 1 Explanation:
$\lambda =\sqrt{\frac{f_y}{f_{cr}}}=\sqrt{\frac{250}{1000}}=0.5$
 Question 2
A steel column is restrained against both translation and rotation at one end and is restrained only against rotation but free to translate at the other end. Theoretical and design (IS:800-2007) values, respectively, of effective length factor of the column are
 A 1.0 and 1.0 B 1.2 and 1.0 C 1.2 and 1.2 D 1.0 and 1.2
GATE CE 2019 SET-2   Design of Steel Structures
Question 2 Explanation:
The given support conditions indicates the following support/ end conditions of column

$l_{eff}$ as per theoretical conditions = 1.0$l_{o}$
$l_{eff}$ as per IS 800 : 2007 = 1.2 $l_{o}$
Considering the errors that may occur due to construction of supports on site.
 Question 3
Consider the following statements for a compression member:

I. The elastic critical stress in compression increases with decrease in slenderness ratio
II. The effective length depends on the boundary conditions at its ends.
III. The elastic critical stress in compression is independent of the slenderness ratio.
IV. The ratio of the effective length to its radius of gyration is called as slenderness ratio

The TRUE statements are
 A II and III B III and IV C II, III and IV D I, II and IV
GATE CE 2009   Design of Steel Structures
Question 3 Explanation:
The elastic critical stress in compression depends on the slenderness ratio,
$\sigma _{ac}=\frac{\pi ^{2}E}{\lambda ^{2}}$
where $\lambda$ is slenderness ratio of the compression member.
 Question 4
The square root of the ratio of moment of inertia of the cross-section to its cross-sectional area is called
 A second moment of area B slenderness ratio C section modulus D radius of gyration
GATE CE 2009   Design of Steel Structures
Question 4 Explanation:
$r=\sqrt{\frac{\text{Moment of inertia}}{\text{Cross-sectional area}}}$
 Question 5
Consider the following statements :

I. Effective length of a battened column in usually increased to account for the additional load on battens due to the lateral expansion of columns.
II. As per IS:800-1984, permissible stress in bending compression depends on both Euler buckling stress and the yield stress of steel.
III. As per IS:800-1984, the effective length of a column effectively held in position at both ends but not restrained against rotation, is taken to be greater than that in the ideal end conditions.

The TRUE statements are
 A Only I and II B Only II and III C Only I and III D I, II and III
GATE CE 2006   Design of Steel Structures
Question 5 Explanation:
The ideal condition is that column is effectively held in position at both ends but not restrained against rotation. IS 800 : 1984 prescribes the same value of effective length as taken for ideal end condition. Hence 3 is false.
 Question 6
A strut in a steel truss is composed of two equal angle ISA $150mm\times 150mm$ of thickness 100 mm connected back-to-back to the same side of a gusset plate. The cross sectional area of each angle is 2921 m$m^{2}$ and moment of inertia ($I_{xx}=I_{yy}$) is 6335000 m$m^{4}$. The distance of the centroid of the angle from its surface ($C_{x}=C_{y}$) is 40.8 mm. The minimum radius of gyration of the strut is
 A 93.2mm B 62.7mm C 46.6mm D 29.8mm
GATE CE 2004   Design of Steel Structures
Question 6 Explanation:

Total cross sectional area
$= 2A =2\times 2921 = 5842 mm^{2}$
The maximum moment of inertia will be about Y-Y axis,
$I_{YY}= 2I_{yi}= 2\times 6335000=12670000 \;mm^{4}$
$r_{min}= \sqrt{\frac{I_{yy}}{2A}}= \sqrt{\frac{12670000}{5842}}= 46.6 mm$
 Question 7
In the design of lacing system for a built-up steel column, the maximum allowable slenderness ratio of a lacing bar is
 A 120 B 145 C 180 D 250
GATE CE 2003   Design of Steel Structures
 Question 8
Consider the following two statements related to structural steel design, and identify whether they are TRUE or FALSE:

I. The Euler buckling load of a slender steel column depends on the yield strength of steel.
II. In the design of laced column, the maximum spacing of the lacing does not depend on the slenderness of column as a whole.
 A Both statements I and II are TRUE B Statement I is TRUE, and statement II is FALSE C Statement I is FALSE, and statement II is TRUE D Both Statements I and II are FALSE
GATE CE 2001   Design of Steel Structures
Question 8 Explanation:
1. Euler's buckling load $=\frac{\pi ^{2}EI}{l^{2}}$
$\; \therefore\,$ Euler's buckling load is independent of yield strength of steel.
2. Maximum spacing of lacing bars shall be such that the maximum slenderness of the main member between adjacent lacing connection should not be greater than 50 or $0.7 \times \lambda _{whole}$.
There are 8 questions to complete.