Two Way Slabs - IS Codes Specification

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Indian Standard codes give following specification for two way slabs for their analysis.

• Case 1: Simply supported slabs which do not have adequate provision to resist torsion at corners, and to prevent the corners from lifting. 

Bending moment for short span,  Mx= Ax.w.Lx^2
Bending moment for long span, My = Ay.w.Ly^2
Where, Ax and Ay are moment co-efficients depending on the ratio Lx/Ly.

• Case 2. Simply supported on the four edges and corners of the slabs are held down.

If Mx and My are maximum bending moments per unit width in the middle strip of the slab in short and long spans respectively, then
                                                   Mx = Ax.w.Lx^2
                                                  My = Ay.w.Ly^2
Where Ax and Ay are co-efficients depending on the ratio Ly/Lx.
At the corners, top and bottom reinforcement should be provided for torsion.

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Structure Engineering notes for GATE and PSUs - part 13

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 Here is our next part for your preparation for the GATE and PSUs examinations.

All information is learned through books and practical exercises.

1. The symmetrical two-hinged parabolic arch when subjected to a uniformly distributed load on the whole span, is subject to normal thrust only.
2. In a two-hinged arch, an increase in temperature induces a maximum bending moment at the crown.
3. The normal thrust at any section of the arch is the component of interacting forces on the section along the tangent to the centerline of the arch.
4. The radial shear at any section of the arch is the component of the interacting forces on the section along the normal to the centerline of the arch.
5. The intercept between a given arch and the linear arch at a section is proportional to the bending moment at the section.
6. A fixed beam AB is subjected to a triangular load varying from zero at end A to 'w' per unit length at end B. The ratio of fixed end moment at end B to that at end A is 3/2.
7. The horizontal thrust due to the rise in temperature in a semi-circular two-hinged arch of radius R is proportional to 1/R2.

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Structure Engineering notes for GATE and PSUs - part 12

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All information is learned through books and practical exercises.

• A T-section is used as a simply supported beam with uniform loading. The maximum bending stress for a given load will occur at the bottom of the section.
• Mohr's circle becomes zero when the both the axial stresses are equal in magnitude and of same nature and both planes being free from shear.
• For beams, I-sections are more economical than rectangular sections because most of the material is concentrated away from the centroid.
• The shear stress distribution over a rectangular cross section of a beam follows a parabolic path.
• Shear stress distribution diagram varies for different cross sectional shapes.
• Bending stress distribution diagram is similar for different sections.
• Polar moment of inertia is sum of MI about the XX and YY axes.
• A cantilever beam of uniform EI has span equal to 'L'. An upward force W acts at the mid point of the beam and a downward force P acts at the free end. In order that the deflection at the free end is zero, the relation between P and W should be W=16P/5.
• If K is defined as the ratio of Young's modulus of elasticity and the permissible stress in compression of a material used in the construction of a column, then the Rankine's constant used in finding the load carrying capacity of columns is proportional to 1/K.

Reference:

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Structure Engineering notes for GATE and PSUs - part 11

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• The allowable tensile stress in structural mild steel plates for steel tank is assumed as 105.5 MPa on net area.
• Steel tanks are mainly designed for water pressure.
• Box type sections should preferably by used at places where torsion occurs.
• The capacity of the smallest pressed steel tank is 1950 litres.
• The bracing between two columns of a steel tanks will be designed to resist horizontal shear due to wind or earthquake + 2.5% of column loads.
• The minimum thickness of plates in a steel stack should be 6 mm.
• Maximum pitch of rivets, used in steel stacks, is limited to 10t, where t is the thickness of the thinner plate being connected.
• The diameter of base of conical flare of a steel stack is more than d, where d is the diameter of the cylindrical part.
• Hudson's formula gives the dead weight of a truss bridge as a function of bottom chord area.
• If the loaded length of span in metres of a railway steel bridge carrying a single track is 6m, then impact factor is taken as between 0.5 to 1.0.
• If the floor is supported at or near the bottom but top chords of a bridge are not braced, then the bridge is called half through bridge.
• The centrifugal force due to curvature of track is assumed to act on the bridge at a height of 1.83 m above the rail level.
• The effect of racking forces is considered in the design of lateral braces.
• When the secondary stresses are taken into account along with primary stresses, then the allowable stress is increased by 96/3%.
• The portal bracing in a truss bridge is used to transfer load from top of end posts to bearings.
• The sway bracing is designed to transfer 50% of the top panel wind load to bottom bracing.
• The bracing provided in the plane of the end posts is called portal bracing.
• The portal bracing is designed for wind force + 5/4% of the compression force in two end posts.
• The pin of a rocker bearing in a bridge is designed for bearing, shear and bending.
• The least dimension in case of a circular column of diameter D is taken as 0.88D.
• In case of timber structures, the form factor for solid circular cross-section is taken as 1.18.
• In case of timber structures, the simple bending formula M-f.z may be applied for rectangular beams up to 300 mm depth.
• The elastic strain of the steel is about 1/12 strain at the initiation of strain hardening and 1/200 of maximum strain.

All information is learned through books and practical exercises.

Reference:

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Structure Engineering notes for GATE and PSUs - part 10

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• Half of the main steel in a simply supported slab is bent up near the support at a distance of l/7 from the center of slab bearing.
• When shear stress exceeds the permissible limit in a slab, then it is reduced by increasing the depth of the beam.
• If the size of panel in a flat slab is 6m * 6m, then as per Indian Standard Code, the widths of column strip and middle strip are 3.0 m and 3.0 m.
• For a slab supported on its four edges with corners held down and loaded uniformly, the Marcus correction factor to the moments obtained by Grashoff Rankine's theory is always less than 1. 
• The permissible diagonal tensile stress in reinforced brick work is about 0.1 N/mm2.
• The limits of percentage p of the longitudinal reinforcement in a column is given by 0.8% to 6%.
• The minimum diameter of longitudinal bars in a column is 12 mm.
• The minimum cover to the ties or spirals should not be less than 25 mm.
• The load carrying capacity of a helically reinforced column as compared to that of a tied column is about 5% more.
• The diameter of ties in a column should be more than 5 mm and also more than one-fourth of diameter of main bar.
• Due to circumferential action of the spiral in a spirally reinforced column both the capacity of the column and ductility of the column increase.
• For heights beyond 6 m counterfort RC walls are preferred over L and T -shaped walls.
• For the design of retaining walls, the minimum factor of safety against over-turning is taken as 2.0

All information is learned through books and practical exercises.

Reference:

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Structure Engineering notes for GATE and PSUs - part 9

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How have you been? Here is our next part for your preparation of GATE and PSUs examinations.

• Strain Energy stored in a member is given by 0.5*Stress*Strain*Volume
• Two identical bars, one simply supported and other fixed at ends, are acted upon by equal loads applied at the midpoints. The ratio of strain energy stored in the simply supported beam and the fixed ended beam is 4.
• If the depth of a beam of rectangular section is reduced to half, strain energy stored in the beam becomes 8 times.
• The specimen in a Charpy impact test is supported as a simply supported beam.
• Impact test enables one to estimate the property of toughness.
• The phenomenon of decreased resistance of a material to reversal of stress is called fatigue.
• The stress below which a material has a high probability of not failing under reversal of stress is known as endurance limit.
• A three hinged parabolic arch rib is acted upon by a single load at the left quarter point. If the central rise is increased and the shape of arch altered at segmental without changing the other details, the horizontal thrust will decrease definitely.
• For ductile materials, the most appropriate failure theory is maximum shear stress theory.
• For the design of a cast iron member, the most appropriate theory of failure is Rankine's theory.
• Principal plane in a uni-dimensional stress system is defined as the plane where Shear stress is zero and normal stress is maximum.
• If an element is subjected to pure shearing stress t, the maximum principal stress is equal to t.

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Reference: Google & A book "Civil Engineering Objective" by S P Gupta and S P Gupta.