As per IS 800:2007, The maximum slenderness ratio for a member normally acting as a tie in a roof truss or a bracing system but subjected to possible reversal of stresses resulting from the action of wind or earthquake forces will be 350.
Slenderness ratio “λ” is given by:
\({\rm{\lambda }} = \frac{{{{\rm{l}}_{{\rm{eff}}}}}}{{{{\rm{r}}_{{\rm{min}}}}}}\)
Where,
r_{min} = minimum radius of gyration of the member, and ℓ_{eff }= effective length of the member
\({{\rm{r}}_{{\rm{min}}}} = \sqrt {\frac{{\rm{I}}}{{\rm{A}}}} = \sqrt {\frac{{\frac{{\rm{\pi }}}{{64}}{{\rm{D}}^4}}}{{\frac{{\rm{\pi }}}{4}{{\rm{D}}^2}}}} = \frac{{\rm{D}}}{4} = \frac{{20}}{4} = 5{\rm{\;mm}}\)
Where,
A = Area of the member and I = Moment of the inertia of the member about its center of gravity
λ = 350
∴ ℓ_{eff} = 350 x 5 = 1750 mmAs per clause 7.7.2 of is 800 : 2007, the battens shall be designed to carry the Bending moments and shear forces arising from transverse shear force (V) equal to 2.5% of the total axial force on the whole compression member.
i) Battens shall be of plates, angles, channels and I sections.
ii) The effective slenderness ratio of the battened column shall be taken as 1.1 times the maximum actual slenderness ratio of the column for the shear deformations.
iii) The thickness of the battens shall not be less than 1/50 th of the distance between the innermost connecting lines between the outermost fasteners.Maximum slenderness ratios for tension members:
Type of Member 
λ 
A tension member in which a reversal of direct stress occurs due to loads other than wind or seismic forces. 
180 
A member normally acting as a tie in roof truss or a bracing system but subjected to a possible reversal of stresses resulting from the action of the wind or earthquake forces. 
350 
Member always under tension 
400 
Maximum slenderness ratios for compression members:
Type of Member 
λ 
A tension member in which a reversal of direct stress occurs due to loads other than wind or seismic forces. 
180 
A member carrying compressive loads resulting from dead loads and imposed loads. 
180 
A member subjected to compressive forces resulting only from combination with wind/earthquake actions, provided the deformation of such members does not adversely affect the stress in any part of the structure. 
250 
Compression flange of a beam restrained against lateraltorsional buckling. 
300 
A member normally acting as a tie in a roof truss or a bracing system not considered effective when subjected to a possible reversal of stresses resulting from the action of wind or earthquake forces. 
350 
Boundary Conditions 
Schematic Representation 
Effective Length 

At one End 
At the Other End 

Translation 
Rotation 
Translation 
Rotation 

Restrained 
Restrained 
Free 
Free 
2.0 L 

Free 
Restrained 
Free 
Restrained 
2.0 L 

Restrained 
Free 
Restrained 
Free 
1.0 L 

Restrained 
Restrained 
Free 
Restrained 
1.2 L 

Restrained 
Restrained 
Restrained 
Free 
0.8 L 

Restrained 
Restrained 
Restrained 
Restrained 
0.65 L 
Concept:
According to Euler’s formula for buckling load,
\({P_{cr}} = \;\frac{{{\pi ^2}EA}}{{{{\left( {\frac{{KL}}{r}} \right)}^2}}}\)
Note:
So, the buckling loadcarrying capacity of a steel column is inversely proportional to the square of the slenderness ratio of the column.
But out of the four options, option 3 is the most appropriate.
The design value of the effective length factor for various combinations is given below:
The effective length of lateral buckling for a simply supported beam under normal loading conditions, provided torsional restraint as fully restrained and warping restraint as both flanges fully restrained should be _______.
The buckling load (Pcr)of a steel column is
\({P_{cr}} = \frac{{{\pi ^2}EI}}{{L_{eff}^2}}\)
where EI = flexural rigidity, Leff = effective length of the column
The effective length of a column (Leff)
It is the length of the column between points of zero moments.
IS:800 – 2007 uses ‘L’ for unsupported length and ‘kL’ for an effective length
where
\(\left\{ {\begin{array}{*{20}{c}} {k = 2,\;for\;a\;cantilever\;column\;}\\ {k = 1,\;for\;both\;ends\;hinged\;column\;}\\ {k = 0.8,\;for\;one\;end\;fixed\;and\;other\;end\;hinged\;}\\ {k = 0.7,\;for\;both\;end\;fixed\;and\; fully\;restraint} \end{array}} \right.\)
Type of member 
Maximum slenderness ratio 
A member carrying compressive loads resulting from the dead load and the imposed load 
180 
A tension member in which a reversal of direct stress occurs due to loads other than wind and seismic forces 
180 
A member subjected to compression force resulting only from combination with wind/earthquake actions, provided the deformation of such members does not adversely affect the stress in any part of the structure 
250 
Compression flange of a beam against lateral torsional buckling 
300 
A member normally acting as a tie in a roof truss or a bracing system not considered effective when subjected to a possible reversal of stress into compression resulting from the action of wind earthquake forces. 
350 
Member always under tension (other than pretensioned members) 
400 
The minimum axial compressive load, P, required to initiate buckling for a pinnedpinned slender column with bending stiffness EI and length L is
Concept:
Ends of the columns:
In this question:
\({P_{min}} = \frac{{{\pi ^2}EI}}{{L{e^2}}}\)
\({P_{min}} = \frac{{{\pi ^2}EI}}{{{L^2}}}\)
Purlin:
The purlins are horizontal beams spanning between the two adjacent trusses. These are the structural members subjected to transverse loads and rest on the top chords of roof trusses. The purlins are meant to carry loads of the roofing material and to transfer it to the panel points.
If the slope of roof truss is not greater than 30' and steel is conforming to grades Fe 4100 or Fe 410W, then, the angle purlins may be designed as an alternate to the general design procedure, as recommended by IS : 8001984.
The splice plate for the steel column is generally designed as:
Explanation:
Column splices:
(i) A splice is a joint provided in the length of the member.
(ii) In the case of column splice, if the load is truly concentric then theoretically no splice is required since compression will be directly transferred through the bearing. But truly axial load in column never occurs.
(iii) Also columns are most of the times also subjected to bending. This raise the necessity of column splices. Column sections are required to be spliced for the following cases
Specification for the design of splices:
(i) Where the ends of the compression members are faced for complete bearing over the whole area there the splices are designed to hold the members accurately in position and to resist any tension where bending is also there.
(ii) In case the connecting members are not faced for complete bearing then splices are designed to transmit all the forces to which they are subjected to.
(iii) Splices are designed as short columns.
Important Points
(i) Ideally a splice plate should be located at a place where flexural moment in the column is zero i.e. at the location of point of contra flexure.
(ii) Due to direct load, there are two points of contra flexure varying from middle of the column to the points above or below the middle.
Concept:
The buckling load in a column is given by
\(P = \frac{{{\pi ^{2\;}}EI}}{{L_e^2}}\)
For a given E, I; the buckling is inversely proportional to the square of the effective length.
When both ends are pinned: P = 200 kN and L_{e} = L
When the column is restrained against lateral movement at its midheight, it creates two columns and each behave as pinned supported and effective length of each column is equal to L/2. (Refer figure)
\(P \propto \frac{1}{{L_e^{2}}}\)
Or
\(PL_e^2 = Constant\)
Or
\(200 \times {L^2} = P \times {\left( {\frac{L}{2}} \right)^2}\)
We get, P = 800 kNIf a rolled steel flat designated as 55 I.S.F. 12 mm is used as lacing, then minimum radius of gyration will be ________.
Concept:
The minimum radius of gyration, \(= \sqrt {\frac{{{I_{min}}}}{A}}\)
Calculation:
Given,
t = 12 mm
For steel flat,
\(\begin{array}{l} {I_{\min }} = \frac{{b{t^3}}}{{12}}\\ A = bt \end{array}\)
\(\sqrt {\frac{{{I_{\min }}}}{A}} = \;\sqrt {\frac{{b{t^3}}}{{12bt}}} = \frac{t}{{\sqrt {12} }} = \frac{{12}}{{\sqrt {12} }} = 3.46\;mm\)Explanation:
Column base:
As per CI. 7.4.1 of IS 800:2007:
Explanation:
Column base:
As per CI. 7.4.1 of IS 800:2007:
Battening is a method of the connecting element of the builtup column.
Batten members are subjected to shear force and bending moment.
A minimum number of battens to be used in a builtup column is equal to four.The design compressive stress of axially loaded compression member in IS 800: 2007 is given by PerryRobertson formula.
IS 800:2007 proposes multiple columns curves in nondimensional form based on PerryRobertson approach.
Also pay attention that:
IS 800: 1984 recommended the use of MerchantRankine formula.
The anchor bolts are provided to check the:
Explanation:
Anchor bolts:
Explanation
If the column ends and gusset materials are not faced/machined for complete bearing, the fasteners are designed for complete bearing, the fasteners are designed for the total forces to be transferred. If they are faced/machined for complete bearing, 50 % of the forces are transferred directly by the column and 50 % through the fasteners.
Column bases are structural elements used in the design of steel structures to transfer the column load to the footings.
Types of Column bases
Slab base
Gusseted base
Note:
Slab bases are used where the columns have independent concrete pedestals. A thick steel base plate and twocleat angles connecting the flanges of the column to the base plate. In addition to these, web cleats are provided to connect the web of the column to the base plate.
These web cleats guard against the possible dislocation of the column during erection. The ends
of the column and also the base plate should be mechanized so that the column load is wholly transferred to the base plate.
Gusseted bases are provided for columns carrying heavier loads requiring large base plates. A gusseted base consists of a base of reduced thickness and two gusseted plates are attached one to each flange of the column.
Concept
The thickness of the slab base is dependent upon the flexural strength of the plate.
A column base consists of a column, a base plate, and an anchoring assembly. In general, they are designed with unstiffened base plates, but stiffened base plates may be used where the connection is required to transfer high bending moments.
Size of Base plate:
(1) Find the bearing strength of concrete which is given by = 0.45 f_{ck}
(2) Therefore, area of base plate required \(= \frac{{{P_u}}}{{0.45\;{f_{ck}}}},\) where P_{u} is factored load.
(3) Select the size of base plate. For economy, as far as possible keep the projection ‘a’ and ‘b’ equal.
Thickness of Base Plate:
(1) Find the intensity of pressure
\(w = \frac{{{P_u}}}{{Area\;of\;base\;plate}}\)
(2) Minimum thickness required is given by
\({t_s} = {\left[ {\frac{{2.5w\left( {{a^2}  {{0.36}^2}} \right){y_{mo}}}}{{{f_y}}}} \right]^{0.5}} > {t_f}\)
Where
t_{s} = thickness of the base plate
and t_{f} = thickness of the flange.
The above formula may be derived by taking μ = 0.3 and using plate theory for finding the bending moment
From the above formula it is clear that the thickness of slab base is dependent upon the flexural strength of the plate.
Explanation:
(i) Column bases should have sufficient stiffness and strength to transmit axial force, bending moments and shear forces at the base of the columns to their foundation without exceeding the load carrying capacity of the supports. Anchor bolts and shear keys should be provided wherever necessary, Shear resistance at the proper contact surface between steel base and concrete/grout may be calculated using a friction coefficient of 0.45.
(ii) The nominal bearing pressure between the base plate and the support below may be determined on the basis of linearly varying distribution of pressure. The maximum bearing pressure should not exceed the bearing strength equal to 0.6f_{ck}, where f_{ck} is the smaller of characteristic cube strength of concrete or bedding material.
(iii) For design of base plate, we will take the value of bearing pressure = 0.45 f_{ck} (As per IS 456, we take design strength of concrete as 0.45 f_{ck}).