Compression Members · Steel Structures · GATE CE

Two steel columns $$P$$ (Length $$L$$ and yield strength $${f_y} = 250\,\,MPa$$) and $$Q$$ (length $$2L$$ and yield strength $${f_y} = 500\,\,MPa$$) have the same cross-sections and end-conditions. The ratio of buckling load of column $$P$$ to that of column $$Q$$ is:

Consider the following statements for a compression member

$${\rm I}.\,\,\,\,$$ The elastic critical stress in compression increases with decrease in slenderness ratio

$${\rm II}.\,\,\,\,$$ The effective length depends on the boundary conditions at its ends

$${\rm III}.\,\,\,\,$$ The elastic critical stress in compression is independent of the slenderness ratio

$${\rm IV}.\,\,\,\,$$ The ratio of the effective length to its radius of gyration is called as slenderness ratio

The TRUE statements are

The square root of the ratio of moment of inertia of the cross-section to its cross-sectional area is called

Consider the following statements

$${\rm I}.\,\,\,\,$$ Effective length of a battened column is usually increased to account for the additional load on battens due to the lateral expansion of columns.
$${\rm II}.\,\,\,\,$$ As per $$IS:$$ $$800$$-$$1984,$$ permissible stress in bending compression depends on both Euler buckling stress and the yield stress of steel.
$${\rm III}.\,\,\,\,$$ 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

In the design of lacing system for a, built-up steel column, the maximum allowable slenderness ratio of lacing bar is

A strut in a steel truss is composed of two equal angles $$ISA$$ $$150mm \times 150mm$$ 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 $$\left( {{{\rm I}_{XX}} = {{\rm I}_{YY}}} \right)$$ is $$6335000$$ $$m{m^4}.$$ The distance of the centroid of the angle from its surface $$\left( {{C_x} = {C_y}} \right)$$ is $$40.8$$ $$mm.$$ The minimum radius of gyration of the strut is

Consider the following two statements related to structural steel design, and identify whether they are True or FALSE.

$${\rm I}.\,\,\,\,\,\,$$ The Euler buckling load of a slender steel column depends on the yield strength of steel.
$${\rm II}.\,\,\,\,\,\,$$ In the design of laced column, the maximum spacing of the lacing does not depend on the slenderness of column as a whole.

Given reason for the following is not more than $$20$$ words

(a) A maximum permissible distance between lacing and battens in steel columns is
$$\,\,\,\,\,\,\,$$ usually specified.
(b) It is sometimes preferable to have unequal flange angle with the longer legs
$$\,\,\,\,\,\,\,$$ horizontal in plate girder.
(c) If two channel sections need to be used as a steel column, they may be connected
$$\,\,\,\,\,\,\,$$ 'face-to-face' rather than 'back-to-back'
(d) It is sometimes preferred to have a small gap between the web and the flange
$$\,\,\,\,\,\,\,$$ plate in a plate girder.
(e) A maximum permissible 'outstand may be specific for flange in built-up sections.

A compound steel column consisting of $$2$$ $$ISHB$$ $$400$$ placed at $$320$$ $$mm$$ centers, carries a total axial load of $$2500$$ $$kN.$$ Minimum slenderness ratio of the compound column is $$30.$$ Width of the flange of one $$ISHB$$ section is $$250$$ $$mm$$ and its minimum radius of gyration is $$51.6$$ $$mm$$. Design a suitable single flat lacing. $$20$$ $$mm$$ diameter single rivet is used to connect the lacings to the column. Rivet capacity need not be calculated. The following table may be used.