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Columns and Struts · Strength of Materials Or Solid Mechanics · GATE CE

Marks 1
9
Marks 2
10
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Marks 1

1

Consider the cross-section of a beam made up of thin uniform elements having thickness t(t << a) shown in the figure. The (x, y) coordinates of the points along the center-line of the cross-section are given in the figure.

GATE CE 2022 Set 1 Strength of Materials Or Solid Mechanics - Columns and Struts Question 2 English

The coordinates of the shear center of this cross-section are :

GATE CE 2022 Set 1
2
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
GATE CE 2013
3
The ratio of the theoretical critical buckling load for a column with fixed ends to that of another column with the same dimensions and material, but with pinned ends, is equal to
GATE CE 2012
4
The effective length of a column of length $$L$$ fixed against rotation and translation at one end is
GATE CE 2010
5
A long structural column (length $$-L$$) with both ends hinged is acted upon by an axial compressive load $$P.$$ The differential equation governing the bending of column is given by: $$$EI{{{d^2}y} \over {d{x^2}}} = - Py$$$

Where $$y$$ is the structural lateral deflection and $$EI$$ is the flexural rigidity. The first critical load on column responsible for its buckling is given by

GATE CE 2003
6
Four column of the same material having identical geometric properties are supported in different ways as shown below GATE CE 2000 Strength of Materials Or Solid Mechanics - Columns and Struts Question 10 English

It is required to order these four beams in the increasing order of their respective first buckling loads. The correct order is given by

GATE CE 2000
7
When a column is fixed at both ends corresponding to Euler's criterion load is
GATE CE 1994
8
The kern area (core) of a solid circular section column of diameter, $$D$$ is a concentric circle of diameter, $$'d'$$ is equal to
GATE CE 1992
9
The axial load carrying capacity of a long column of given material. Cross-sectional area, $$A$$ and length, $$L$$ is governed by
GATE CE 1992

Marks 2

1

A homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio (l/r) of 105, where l is the bar length and r is the radius of gyration. The coefficient of thermal expansion of steel is $12 \times 10^{-6}$ $^{\circ}$C. Consider the effective length of the steel bar as $0.5l$ and neglect the self-weight of the bar.

The differential increase in temperature (rounded off to the nearest integer) at which the bar buckles is

GATE CE 2024 Set 2
2
Consider two axially loaded columns, namely. $$1$$ and $$2,$$ made of a linear elastic material with Young's modulus $$2 \times {10^5}\,\,MPa,$$ square cross-section with side $$10$$ $$mm$$, and length $$1$$ $$m.$$ For Column $$1,$$ one end is fixed and the other end is free. For column $$2,$$ one end is fixed and the other end is pinned. Based on the Euler's theory, the ratio (up to one decimal place) of the buckling load of Column $$2$$ to the buckling load of column $$1$$ is ___________
GATE CE 2017 Set 1
3
If the following equation establishes equilibrium in slightly bent position, the mid-span deflection of a member shown in the figure is
$${{{d^2}y} \over {d{x^2}}} + {P \over {EI}}y = 0$$ GATE CE 2014 Set 1 Strength of Materials Or Solid Mechanics - Columns and Struts Question 4 English

If $$'a'$$ is amplitude constant for $$y,$$ then

GATE CE 2014 Set 1
4
The sketch shows a column with a pin at the base and rollers at the top. It is subjected to an axial force $$P$$ and a moment $$M$$ at mid-height. The reaction$$(s)$$ at $$R$$ is/are GATE CE 2012 Strength of Materials Or Solid Mechanics - Columns and Struts Question 5 English
GATE CE 2012
5
Cross-section of a column consisting of two steel strips, each of thickness $$t$$ and width $$b$$ is shown in the figure below. The critical loads of the column with perfect bond and without bond between the strips are $$P$$ and $${P_0}$$ respectively. The ratio $$P/{P_0}$$ is GATE CE 2008 Strength of Materials Or Solid Mechanics - Columns and Struts Question 6 English
GATE CE 2008
6
A rigid bar $$GH$$ of length $$L$$ is supported by a hinge and a spring of stiffness $$K$$ as shown in the figure below. The buckling load, $${P_{cr}}'$$ for the bar will be GATE CE 2008 Strength of Materials Or Solid Mechanics - Columns and Struts Question 7 English
GATE CE 2008
7
A steel column, pinned at both ends, has a buckling load of $$200$$ $$kN.$$ If the column is restrained against lateral movement at its mid-height, its buckling load will be
GATE CE 2007
8
The buckling load $$P = {P_{cr}}$$ for the column $$AB$$ in figure, as $${K_T}$$ approaches infinity, becomes $$\alpha {{{\pi ^2}E{\rm I}} \over {{L^2}}}$$ GATE CE 2006 Strength of Materials Or Solid Mechanics - Columns and Struts Question 3 English

Where $$\alpha $$ is equal to

GATE CE 2006
9
The maximum tensile stress at the section $$X$$ - $$X$$ shown in the figure below is GATE CE 2005 Strength of Materials Or Solid Mechanics - Columns and Struts Question 8 English
GATE CE 2005
10
A rigid rod $$AB$$ of length $$L$$ is hinged at $$A$$ and is maintained in its vertical position by two springs with spring constants $$K$$ attached at end $$B.$$ The system is under stable equilibrium under the action of load $$P$$ when $$P < \,{P_{Cr}}$$. The system will be in unstable equilibrium when $$P$$ attains a value greater than GATE CE 1990 Strength of Materials Or Solid Mechanics - Columns and Struts Question 9 English
GATE CE 1990
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