GATE 2006 Civil Engineering

In the design of beams for the limit state of collapse in flexure as per $$IS:$$ $$456$$ - $$2000,$$ let the maximum strain in concrete be limited to $$0.0025$$ (in place of $$0.00...

Assuming concrete below the neutral axis to be cracked, the shear stress across the depth of a singly-reinforced rectangular beam section

Consider the following statements: $$1.\,\,\,\,\,\,$$ The width-to-thickness ratio limitations on the plate elements under $$\,\,\,\,\,\,\,\,\,\,\,$$ compression in steel members a...

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 e...

In the design of welded tension members, consider the following statements: $${\rm I}.\,\,\,\,\,\,\,\,\,$$ The entire cross-sectional area of the connected leg is assumed to contri...

The directional derivative of $$\,\,f\left( {x,y,z} \right) = 2{x^2} + 3{y^2} + {z^2}\,\,$$ at the point $$P(2,1,3)$$ in the direction of the vector $${\mkern 1mu} \vec a = \wideha...

In the design of beams for the limit state of collapse in flexure as per $$IS:$$ $$456$$ - $$2000,$$ let the maximum strain in concrete be limited to $$0.0025$$ (in place of $$0.00...

Using Cauchy's Integral Theorem, the value of the integral (integration being taken in counter clockwise direction) $$\int\limits_C {{{{z^3} - 6} \over {3z - i}}} dz$$ is where C i...

Solution for the system defined by the set of equations $$4y+3z=8, 2x-z=2$$ & $$3x+2y=5$$ is

For a given matrix $$A = \left[ {\matrix{ 2 & { - 2} & 3 \cr { - 2} & { - 1} & 6 \cr 1 & 2 & 0 \cr } } \right],$$ one of the eigen value is $$3.$$ The other two eigen values are

The solution of the differential equation $$\,{x^2}{{dy} \over {dx}} + 2xy - x + 1 = 0\,\,\,$$ given that at $$x=1,$$ $$y=0$$ is

As per $$IS:$$ $$456$$-$$2000,$$ consider the following statements: $$1.$$ The modular ratio considered in the working stress method depends on the type of steel used. $$2.$$ There...

Mohr's cicle for the state of stress defined by $$\left[ {\matrix{ {30} & 0 \cr 0 & {30} \cr } } \right]$$ $$MPa$$ is a circle with

A long shaft of diameter $$d$$ is subjected to twisting moment $$T$$ at its ends. The maximum normal stress acting at its cross-section is equal to

A thin-walled long cylindrical tank of inside radius $$'r'$$ is subjected simultaneously to internal gas pressure $$P$$ and axial compressive force $$F$$ at its ends. In order to p...