GATE CE 1998
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GATE CE

1
Solve $${{{d^4}y} \over {d{x^4}}} - y = 15\,\cos \,\,2x$$
2
$${\left( {s + 1} \right)^{ - 2}}$$ is laplace transform of
3
The Laplace Transform of a unit step function $${u_a}\left( t \right),$$ defined as
$$\matrix{ {{u_a}\left( t \right) = 0} & {for\,\,\,t < a\,} \cr { = 1} & {for\,\,\,t > a,} \cr } $$ is
4
The continuous function $$f(x, y)$$ is said to have saddle point at $$(a, b)$$ if
5
The Taylor's series expansion of sin $$x$$ is ______.
6
A discontinuous real function can be expressed as
7
Obtain the eigen values and eigen vectors of $$A = \left[ {\matrix{ 8 & -4 \cr 2 & { 2 } \cr } } \right].$$
8
The real symmetric matrix $$C$$ corresponding to the quadratic form $$Q = 4{x_1}{x_2} - 5{x_2}{x_2}$$ is
9
If $$A$$ is a real square matrix then $$A{A^T}$$ is
10
In matrix algebra $$AS=AT$$ ($$A,S,T,$$ are matrices of appropriate order) implies $$S=T$$ only if
11
The microbial quality of treated piped water supplies is monitored by
12
Water distribution systems are sized to meet the
13
The return period for the annual maximum flood of a given magnitude is 8 years. The probability that this flood magnitude will be executed once during the next 5 years is
14
The cross-section of a pretensioned pre-stressed concrete beam is shown in Figure. The reinforcement is placed concentrically. If the stress in steel at transfer is $$1000$$ $$MPa,$$ compute the stress in steel immediately after transfer. The modular ratio is $$6.$$ GATE CE 1998 Reinforced Cement Concrete - Prestressed Concrete Question 5 English
15
An isolated $$T$$ beam is used as a walkway. The beam is simply supported with an effective span of $$6$$ $$m.$$ The effective width of flange, for the cross-section shown in figure, is GATE CE 1998 Reinforced Cement Concrete - Flanged Beams Question 1 English
16
The cross-section of a simply supported plate girder is shown in figure. The loading on the girder is symmetrical. The bearing stiffeners at supports are the sole means of providing restraint against torsion. Design the bearing stiffeners at supports, with minimum moment of inertia about the center line of web plate only as the sole design criterion. The flat sections available are: $$250 \times 25,\,\,250 \times 32,\,\,\,200 \times 28$$ and $$200 \times 32\,\,mm.$$ Draw a sketch GATE CE 1998 Steel Structures - Plate Girder Question 1 English
17
A cantilever beam is shown in the figure. The moment to be applied at free end for zero vertical deflection at the point is GATE CE 1998 Strength of Materials Or Solid Mechanics - Deflection of Beams Question 4 English
18
The stiffness matrix of a beam element is given as $${{2EI} \over L}\left[ {\matrix{ 2 & { + 1} \cr { + 1} & 2 \cr } } \right].$$ Then the flexibility matrix is
19
The steel portal frame shown in figure is subjected to an imposed service load of $$15$$ $$kN$$. Compute the required plastic moment capacity of the members. All the members are of the same cross-section. Draw the collapse load. GATE CE 1998 Structural Analysis - Plastic Analysis Question 3 English
20
The plastic modulus of a section is $$4.8 \times {10^{ - 4}}\,\,{m^3}.$$ The shape factor is $$1.2$$. The plastic moment capacity of the section is $$120$$ $$kN$$-$$m.$$ The yield stress of the material is
21
The strain energy stored in member $$'AB'$$ of the pin jointed truss shown aside when $$'E'$$ and $$'A'$$ are same for all members is GATE CE 1998 Structural Analysis - Energy Principle Question 13 English
22
A three hinged arch shown in Figure is quarter of a circle. If the vertical and horizontal components of reaction at $$A$$ are equal, the value of $$\theta $$ is GATE CE 1998 Structural Analysis - Arches and Cable Question 5 English
23
For a highway with a design speed of 100kmph, the safe OSD is assume acceleration as 0.53 $$m/sec^2$$. the road is two lane with two way traffic. User other specifications as per IRC
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