Structural Steel and MetalsCivil Engineering
Steel
- Steel is an alloy of iron and carbon, along with small amounts of other alloying elements or residual elements as well. The plain iron-carbon alloys (Steel) contain 0.002 - 2.1% by weight carbon. For most of the materials, it varies from 0.1-1.5%.
There are 3 types of plain carbon steel:
- (i) Low-carbon steels: Carbon content in the range of < 0.3%
- (ii) Medium carbon steels: Carbon content in the range of 0.3 – 0.6%.
- (iii) High-carbon steels: Carbon content in the range of 0.6 – 1.4%.
Properties
Resistance to corrosion:
- Is the ability of a material that resists against reaction with caustic elements that corrode or degrade the material.
Ultimate Strength:
- The maximum strength the material can withstand without breaking.
Hardness
- It is defined as the resistance of a material to penetration or permanent deformation. It usually indicates resistance to abrasion, scratching, cutting or shaping.
Ductility
- It is the ability of a material to withstand tensile force when it is applied upon it as it undergoes plastic deformation, this is often characterized by the material's ability to be stretched into a wire.
- With increase in carbon content the strength, hardness and brittleness increases but the ductility and toughness decreases.
- Because with increase in carbon the cementite phase in the material increases and since cementite is hard and brittle so the ductility decreases with an increase in carbon.
Prying force:
- The flexibility of connected parts can lead to deformations that increases the tension applied to the bolts. The additional tension is called prying force. The prying forces can be kept small can be kept small by using a thick plate or by limiting the distance between the bolt and plate edge.
- Note: Prying force do not develop in case of ordinary bolts, since when bolt failure takes place contact between the two connecting plates is lost.
Fillet weld
- When filet weld is applied to the square edge of member, the maximum size of weld should be less than the edge thickness by at least 1.5 mm.
- When fillet weld is applied to the round toe of rolled steel sections, the maximum size of the weld should not exceed ¾ of the thickness of the section at the toe.
- When fillet weld is used for lap joint, then overlap of the members connected should not be less than five times thickness of thinner part.
Types of beam connection:
- Two or more beams at a junction are connected each other using either flange or web clips.
Framed Connection:
- Framed connection are usually connected through web cleats only as shown in the figure below:
 |
| Framed beam connection |
Stiffened and unstiffened beam seated connections are depicted in the figure below:
- It can be clearly observed, the unstiffened connection requires flange cleat only, and an additional connecting member is used for stiffened connection.
 |
| Stiffened and Unstiffened connection |
The relation between nominal and bolt hole diameter is given below:
- Nominal diameter Hole size
- 12 - 14 mm 1 mm extra
- 16 - 24 mm 2 mm extra
- > 24 mm 3 mm extra
 |
| Pitch and edge Distance |
- P min = 2.5 × dn , dn = nominal diameter
- e min = 1.5 × dh , dh = diameter of hole
Reduction factor if packing plates are used (βpk):
- The design shear capacity of bolts carrying shear through a packing plate in excess of 6 mm shall be decreased by a factor, β given by:
- βpk = 1-0.0125tpk
- where, tpk = Thickness of thicker packing, in mm
Built-up Section- :
- In a built-up section carrying tensile force, the flanges of two channels are turned outward to have greater lateral rigidity.
- Built up section is made by joining or combining two or more sections to have a section of required strength as per the design criteria. It can be combined by welding or bolting.
- Here the flanges of the channel sections are kept outward to have a better lateral rigidity.
- Sometimes rolled steel sections do not fulfill the design criteria. In such situations built-up sections can be used.
Strength of weld
- The strength of the smaller width plate will be calculated as it has the least area and thus the least strength.
- Strength of weld, P = (Permissible stress in weld) × (Area of weld)
- ∴ Where,
- lw = Effective length of weld
- fu = smaller of ultimate strength of weld and the parent material
- tt = throat thickness
- Pdw = design strength of weld
- γmw = partial safety factor
- = 1.25 (shop welding)
- = 1.25 (site welding)
slenderness ratio of steel sections
| Member | Maximum Effective Slenderness ratio |
|
|---|---|---|
| Pure Compression Member | 180 | |
| Pure tension Member | 400 | |
| Tension Member subjected to reversal of stress due to loads other than wind and earthquake. | 180 | |
| Tension Member subjected to reversal of stress due to wind or earthquake load. | 350 | |
| A member subjected to compression forces resulting from wind or earthquake forces provided that deformation of such member does not affect the stress in any part of structure. | 250 | |
| Compression flange of beam against lateral torsional buckling | 300 |
Compression member:
- A compression member is a structural member which is straight and subjected to two equal and opposite compressive forces applied at its ends. Different terms are used for compression member depending upon its position in the structure.
- Strut → It is used in roof truss and bracing
- Column/Stanchion/post → It supports floors or girders in the building
- Principal rafter → It is a top chord member in a roof truss
- Boom → It is a principal compression member in a crane
Ideal compression member:
- The most important property of the section in a compression member is the radius of gyration and thus the moment of inertia and it can be increased by spreading the material of section away from the axis.
- An ideal section is one which has the same moment of inertia about any axis through its center of gravity.
Slenderness Ratio, SR = Lex/rxx
Shear key:
- The main purpose of the installation of shear keys is to increase the extra passive resistance developed by the height of shear keys. However, active pressure developed by shear keys also increases simultaneously.
- The success of shear keys lies in the fact that the increase of passive pressure exceeds the increase in active pressure, resulting in a net improvement of sliding resistance.
- The retaining wall is not safe against sliding, hence the shear key is provided resulting in a net improvement of sliding resistance
A counterfort retaining wall
- A counterfort retaining wall is a cantilever wall with counterforts, or buttresses, attached to the inside face of the wall to further resist lateral thrust.
- In the counterfort retaining wall, the stem and the base and the base slab are tied together by counterforts, at suitable intervals
- Because of the provision of counterforts, the vertical stem, as well as the heel slab, acts as a continuous slab, in contrast to the cantilevers of cantilever retaining wall
- Counterforts are firmly attached to the face slab as well as the base slab; The earth pressure acting on the face slab is transferred to the counter forts which deflect as vertical cantilevers
- The back of the rear counter forts comes in tension and their front face is under compression
- Hence the inclined (back) face of rear counter forts should be provided with main reinforcement and in front counterforts, the tension develops at the bottom face so it is provided with main reinforcement
- Counterfort retaining walls are economical for height over about 6m
Gravity Dam
- A gravity dam is defined as a structure which is defined in such a way that its own weight resists the external forces.
- Maximum possible height (limiting height) of the dam is given by:
- Hmax= f/γw(Sc+1)
- A low gravity dam is the one whose height is less than Hmax.
- A high gravity dam is the one whose height is greater than Hmax.
- A gravity dam is called as low dam if the base width is designed from the consideration of the resultant falling as close as possible to the extremities of the middle third of the base.
For No tension Failure
- width of Dam = H / (underoot G-C)
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
When the available length of the structural steel section is less than the required length of the column.
- In case of multi-storey buildings, the section of column required for the various storeys may be different.
- In multi-storeyed buildings, for convenience of fabrication, it is kept at about 5 m lengths. So, splicing of column is necessary to join the fabrication along the length.
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.
- (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.
Properties of Aluminium:
1. It is a very good conductor of heat and electricity.
2. It is a silvery-white metal with a bluish tinge and it exhibits bright lustre on a freshly broken surface.
3. It is a non-magnetic substance.
4. It is rarely attacked by nitric acid, organic acid or water. It is highly resistant to corrosion.
5. It is light in weight, malleable and ductile.
6. It possesses great toughness and tensile strength.
7. Its specific gravity is 2.7
Modulus of elasticity (GPa) and Coefficient of thermal expansion ( 10-6 m/m ° C)
Steel 200 and 11-13
Aluminium 69 and 23-24
Local Buckling: The individual elements of a compressive member such as flange, web etc may buckle locally.
The width to thickness ratio for single angle section of class 1 to prevent local buckling (compression due to bending) is 9.4ϵ
ϵ = √ 250/fy
As per IS 800:2007 clause 17.2.2.1, In bearing type of connections, the holes may be made not more than 1.5 mm greater than the diameter of the bolts in case of bolts of diameter less than 25 mm and not more than 2 mm in case of bolts of diameter more than 25 mm, unless otherwise specified by the engineer.
Net area of block shear =(L−(n−1)d−d/2)×t
Where, Length as shown in figure
n = number of bolts
d = dia of hole
t = thickness of plate
Strength of bolt in double shear
Strength of bolt in bearing
The battened strut is a compressive member and effective length for compression members under different end conditions is given as:
Degree of end restraint | Theoretical value | Recommended value |
Effectively held in position and restrained against rotation at both ends. | 0.50L | 0.65L |
Effectively held in position and restrained against rotation at one end | 0.70L | 0.80L |
Effectively held in position at both ends, but not restrained against rotation. | 1.00L | 1.00L |
Effectively held in position and restrained against rotation at one end and at other end restrained against rotation but not held in position | 1.00L | 1.20L |
Effectively held in position and restrained against rotation at one end and at other end partially restrained against rotation but not held in position | - | 1.50L |
Effectively held in position at one end but not restrained against rotation and at other end restrained against rotation but not held in position. | 2.00L | 2.00L |
Effectively held in position and restrained against rotation at one end and at other end not held in position and not restraint against rotation. | 2.00 L | 2.00L |
Where L is the unsupported length of column.
For battened struts, the effective length should be increased by 10%.
∴ The effective length of a battened strut of actual length L, effectively held in position both ends but not restrained in direction, is taken as 1.1L
Lug Angle
When tension member is subjected to heavy load, the number of bolts or length of weld required for making connection becomes large and results in uneconomical size of gusset plate. In such situations, additional short angles called ‘lug angles’ may be used.
Lug angle is small piece of angle used to connect outstand legs of the members to the gusset plate. The purpose of lug angle is to reduce the length of connection to the gusset plate and to reduce shear lag effect.
Shear Lag:
The larger the unconnected leg, less is the transfer of tensile stress. This effect of uneven strain distribution in unconnected flange at connection is called shear lag.
For elementary profile of the dam,
Base width of the dam is given by:
When uplift is ignored, C =0
Since the member is a tie member, therefore the maximum slenderness ratio will be 400 (for a member always tension maximum slenderness ratio is 400).
Specifications of Pitch of rivet:
Pitch is the distance between two adjacent rows of rivet parallel to the direction of application of force. The minimum pitch will be 2.5 times the gross diameter.
The minimum pitch should not be less than 2.5 times the nominal diameter of the rivet.
As a thumb rule pitch equal to 3 times the nominal diameter of the rivet is adopted.
The maximum pitch shall not exceed 32 times the thickness of the thinner outside plate or 300 mm whichever is less.
Bearing stiffeners are provided at supports and at all locations where concentrated load is acting. They are provided to prevent the web crippling at supports, where bearing occurs and location of concentrated loads, where buckling occurs.
Bearing area is calculated at root of web by dispersion at a slope of 1:2.5 and buckling area is calculated at neutral axis by dispersion at 450. Hence, both are different. (Refer the following figure).
Gravity Dam
A gravity dam is defined as a structure which is defined in such a way that its own weight resists the external forces.
Maximum possible height (limiting height) of the dam is given by:
Hmax=fγ/w(Sc+1)
A low gravity dam is the one whose height is less than Hmax.
A high gravity dam is the one whose height is greater than Hmax.
A gravity dam is called as low dam if the base width is designed from the consideration of the resultant falling as close as possible to the extremities of the middle third of the base.
As per IS 800:2007 clause 17.2.2.1, In bearing type of connections, the holes may be made not more than 1.5 mm greater than the diameter of the bolts in case of bolts of diameter less than 25 mm and not more than 2 mm in case of bolts of diameter more than 25 mm, unless otherwise specified by the engineer.
Net area of block shear =(L−(n−1)d−d/2)×t
Where, Length as shown in figure
n = number of bolts
d = dia of hole
t = thickness of plate
Compression Member:
They are primarily designed for axial load where slenderness ratio and minimum radius of gyration plays a major role for suitability of a section as compression member.
More the minimum radius of gyration means less the slenderness ratio, so more the axial capacity and more suitability of the section as compression member.
Double angle section: When two angle sections are connected with each other in any configuration is termed as double angle section.
Equal angles on the same side of the gusset plate: It has a very low radius of gyration about the axis parallel to gusset plate and it acts as weak axis for buckling, hence least preferred.
Equal angles on the opposite side of the gusset plate: It is good compared to equal angles on the same side as no weak axis w.r.t. radius of gyration. But its axial capacity is less compared to unequal double angles.
Unequal angles with short legs back to back: It has slightly improved axial capacity compared to equal sections but has a low radius of gyration about the axis perpendicular to the short edges, hence not preferred.
Unequal angles with long legs back to back: It has slightly improved axial capacity compared to equal sections and does not have a weak axis for buckling, hence it is best preferred section among the double angles sections. It has larger value of radius of gyration.
Important Point:
Generally angle sections (single or double) are least preferred as compression member. Mostly I sections, channel sections, tubular section, box sections are used for compression member. Among all the sections tubular sections are most efficient, economical and best preferred sections for compression member.
The most economical section for a steel column is
Tubular section is best suited and most economical for the design of smaller compression member subjected to smaller load.
Various reasons are as follows:
1. Round tubes have the same radius of gyration in all directions and have a high local buckling strength. These are usually very economical unless moments are too large for the sizes available.
2. Tube has excellent torsional resistance.
3. In the case of members subjected to wind, round tubes are subjected to less force than flat sections.
4. They have less surface area to paint or fireproof.
5. Tubes do not have the problem of dirt collection or cleaning.
6. The weight of tube sections usually is less than one half the weight required for open profile sections. Although tube sections cost about 25 percent more than open sections, but about 20 percent of cost savings can still be achieved.
It can be seen that only the tubular section has the same moment of inertia about any axis through its center of gravity, hence The tubular section is the ideal compression member.
When the end of the column is machined for full bearing on base plate, it is assumed that 50 % of the total design axial column load is transferred to base plate by direct bearing and remaining 50% of axial load will be transferred through fastenings like bolted or welded connection including gusset plate, stiffeners if any.
However, when the end of column and gusset plate are not machined for full bearing i.e. partially machined, in that case it is assumed that connection to base plate are designed for all the forces acting on plate.
The lacing shall be proportioned to resist a total transverse shear, (Vt), at any point in the member, equals to at least 2.5 percent of the axial force in the member and shall be divided equally among all transverse lacing systems in parallel planes.
When placing a fillet weld, though the welder tires to build up the weld to its full dimension from the beginning, there is always slight tapering off where the weld starts and ends. The width of this tapering is called end returns and is equal to two times the size of weld on either side of welding. This tapered portion of weld is not able resist or carry any load hence cannot be the part of weld length. Therefore, the length of weld which is actually effective to resist loads, called effective length, is taken as overall length of weld minus two times the size of weld in case fillet weld as per IS 800:2007 codal provisions.
Important point:
The minimum value of effective length as per codal provisions of IS 800:2007 for different type of welding is shown below in tabulated form:
Type of Weld | Definition of Effective length | Minimum Effective length |
Groove Weld | Effective length is the length of continuous full size weld. | Four times the size of weld. |
Fillet Weld | Effective length is taken as overall length of weld minus two times the size of weld. | Width of plate. |
Intermittent Fillet Weld | Effective length is taken as overall length of weld minus two times the size of weld | Maximum (4S, 40 mm); where S is the size of weld. |
For steel members exposed to weather and not accessible for repainting, the thickness of steel
Following are the specifications for steel member exposed to weather:
When the steelwork is directly exposed to weather and is fully accessible for cleaning and repainting the thickness shall not be less than 6 mm.
When the steelwork directly exposed to weather and is not accessible for cleaning and repainting the thickness shall not be less than 8 mm.
When the steelwork is not directly exposed to weather, the thickness of steel in main members shall not be less than 6 mm.
When the steelwork is not directly exposed to weather, the thickness of steel in secondary members shall not be less than 6 mm.
Throat thickness of Weld
The Value of Effective throat thickness either depends upon K values which depend on the angle between fusion faces or depend upon the size of the weld.
Throat Thickness (Tt) = K × Size of the weld
The K values vary as mentioned in the table below
Angle between fusion faces (in degrees) | 60 to 90 | 91 to 100 | 101 to 106 | 107 to 113 | 114 to 120 |
K | 0.7 | 0.65 | 0.6 | 0.55 | 0.5 |
Fillet welded joint
By Working stress method
Ps = Lw × t × τv
Buckling
Buckling is a phenomena wherein a compression member is subjected to bending stress because of unintended eccentricities of axial compression force, it causes the compression member to bend out of the axis leading to further increase in stress causing the member to ultimately fail.
Lateral torsional buckling
Lateral torsional buckling may occur in an unrestrained beam. When I sections are used as beams or beam columns, the compression flange is under compressive stress and has a tendency to buckle but it is attached to the tension flange which resists the buckling giving rise to torsion within the beam section. This torsion twists and warps the unrestrained part of beam leading to lateral torsional buckling.
The best way to prevent this type of buckling from occurring is to restrain the flange under compression, which prevents it from rotating along its axis.
Riveted Joint:
A riveted joint is a permanent joint which uses rivets to fasten two materials.
Types of riveted joints:
1. Lap Joint
A lap joint is that in which one plate overlaps the other and the two plates are then riveted together.
Number of shearing planes = 1
2. Butt joint
A butt joint is that in which the main plates are kept in alignment butting each other and a cover plate is placed either on one side or on both sides of the main plates. The cover plate is then riveted together with the main plates.
Number of shearing plane in single cover butt joint = 1
Number of shearing plane in double cover butt joint = 2
Concept of shearing strength:
Strength of joint per pitch length in shearing, Pd = Ps × N × n
Where, Ps = Strength of one rivet in single shear, n = Number of shearing planes, N = Number of rivets
maximum projection of bearing stiffeners attached a steel beam of web thickness, tw
According to IS 800, clause no. 8.7.1.5,
The buckling resistance should be based on the design compressive stress of a strut, the radius of gyration being taken about the axis parallel to the web. The effective section is the full area or core area of the stiffener together with an effective length of web on each side of the centreline of the stiffeners, limited to 20 times the web thickness. The design strength used should be the minimum value obtained for buckling about the web or the stiffener.
Maximum permissible direct tensile stress in structural steel is 0.60 fy
Maximum permissible direct compressive stress in structural steel is 0.60 fy
Maximum permissible bending tensile stress in structural steel is 0.66 fy
Maximum permissible bending compressive stress in structural steel is 0.66 fy
Maximum permissible average shear stress in structural steel is 0.40 fy
Maximum permissible bearing stress in structural steel is 0.75 fy
Maximum Permissible average shear stress in structural steel= 0.4 fy
Design of Deep Beam
Factors considered in design of deep beams:
1. The deep beam is considered as vertical plate subjected to loading in its own plane due to which it can bend or buckle laterally.
2. For analysis purpose, it is treated as 2D plane stress problem.
3. Due higher depth of deep beams, shear deformations cannot be neglected and their contribution becomes significant which in turn results non uniform strain and stress distribution along the depth of deep beam.
4. The effect of temperature stresses are also considered in designing of deep beam because when deep beams subjected to high heat and then rapidly cooling reduces the strength and increases the deflection.
Important point:
Let L = effective span and D = Overall Depth
As per IS 456: 2000 Codal provisions, a beam is considered to be deep beam if:
L/D<2 For simply supported beams
L/D<2.5 For continuous beams
Lacing of steel memeber
As per IS 800 Design specifications of lacing are:
1. The angle of inclination of the lacing with the longitudinal axis of the column should be between 40° to 70°.
2. The slenderness ratio of the lacing bar should not exceed 145.
3. Minimum width of lacing in riveted connections should be:
ϕ (mm) 22 20 18 16
Width (mm) 65 60 55 50
Which is approximated to 3 times the nominal diameter.
Note: The inclination of lacing bars with the axis of the compressive member should be more than 40° and less than 70°.
Splicing of Column: Splicing is nothing but joining of same material in successive runs along their lengths. The length of structural steel members as available in the market or site is limited up to 15 m maximum or even less. So whenever available length structural steel section is less than required length of the column splicing becomes necessary.
Splicing of column is necessary in the following cases:
When the available length of structural steel section is less than the required length of the column.
In case of multi-storey buildings, the section of column required for the various storeys may be different.
In multi-storeyed buildings, for convenience of fabrication it is kept at about 5 m lengths. So, splicing of column is necessary to join the fabrication along the length.
Vertical Deflection limits for industrial buildings as per IS 800:2007 are:
a) For Purlins and Girts subjected to live load/wind load supported on elastic cladding, maximum deflection is limited to span / 150.
b) For Purlins and Girts subjected to live load/wind load supported on Brittle cladding, maximum deflection is limited to span / 180.
As per IS 800: 2007, Cl 12.8.2, following codal provisions regarding bracing should be remembered.
1. Braced cross-section shall be plastic.
2. The tension braces will able to resist between 30 to 70 percent of the load for lateral loading in either direction.
3. The required compressive strength of bracing member shall not exceed the design strength in axial
Compression.
4. The slenderness ratio for a bracing member in case of hangers shall not exceed 160.
Note:
A bracing member is subjected to tension as well as compressive loads. If such member is designed for compression called lacing member. The maximum slenderness ratio of lacing member is 145.
The moment capacity of the base plate is given by,
Bearing strength of bolt is given by:
Pb = 2.5 × kb × (d × t) × fu
where ‘t’ is the thickness of thinner main plate and cover plate
Where
e = edge distance
dh = diameter of hole
p = pitch
fub = ultimate bearing strength of bolt
fu = ultimate bearing strength of plate
kb depends upon edge distance, pitch distance, bolt hole diameter, ultimate strength of the bolt and ultimate strength of the plate
A gravity dam is constructed from concrete or stone masonry and designed to hold back water pressure by primarily utilizing the weight of the material alone to resist the horizontal pressure of water pushing against it. Gravity dams are designed so that each section of the dam is stable, independent of any other dam section.
∴ Water pressure on the upstream face is the main destabilizing (or overturning) force acting on a gravity dam.
Where An: net area; Ag: gross area, fy: yield stress; fu:ultimate stress;Ym1: partial safety against ultimate stress factor: Ym0: partial safety factor against yield and buckling
As per IS 800: 2007, Clause 6.3.1
The design strength in tension of a plate, Tdn as governed by rupture of net cross – sectional area An at the hole is given by
Tdn = 0.9An.fu/γm
where
γm1 = partial safety factor for failure at ultimate stress
fu = ultimate stress of the material
An = net effective area of the member
Counterfort Retaining Wall
A counterfort retaining wall is a cantilever wall with counterforts, or buttresses, attached to the inside face of the wall to further resist lateral thrust. The use of this counter fort is to reduce the shear force, and the bending moment in the vertical steam of the slab.
Design of counterfort retaining wall:
In a counterfort retaining wall, the vertical slab is designed as a continuous slab and the heel slab is designed as a continuous slab because this will reduce joint efficiency hence an extra margin is created. But this will increase the cost also.
Concept:
A counterfort retaining wall is a cantilever wall with counterforts, or buttresses, attached to the inside face of the wall to further resist lateral thrust.
In the counterfort retaining wall, the stem and the base and the base slab are tied together by counterforts, at suitable intervals
Because of the provision of counterforts, the vertical stem, as well as the heel slab, acts as a continuous slab, in contrast to the cantilevers of cantilever retaining wall
Counterforts are firmly attached to the face slab as well as the base slab; The earth pressure acting on the face slab is transferred to the counter forts which deflect as vertical cantilevers
The back of the rear counter forts comes in tension and their front face is under compression
Hence the inclined (back) face of rear counter forts should be provided with main reinforcement and in front counterforts, the tension develops at the bottom face so it is provided with main reinforcement
Counterfort retaining walls are economical for height over about 6m
∴ In a counterfort retaining wall, the main reinforcement is provided on the bottom face in front counterfort and inclined face in back counterfort.
Battens
As 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.
Laced Column
For the design of laced columns:
I) The sections to be laced are so spaced that the radius of gyration of the section about the axis perpendicular to the plane of lacing is not less than the radius of gyration about the axis in the plane of lacing.
II) The effective slenderness ratio should be taken as 1.05 times the actual maximum slenderness ratio, in order to account for shear deformation effect.
III) Angle of inclination of lacing bar should be kept between 40° - 70°. Lacing is most efficient between 35° to 45°, but angle less than 40° would result in a higher length of lacing bar which may then to buckle individually.
IV) The maximum spacing of the lacing bar should be such that the minimum slenderness ratio of the component member should not be greater than 50 or 0.7 times the slenderness ratio of the member.
V) The lacing for compression members should be proportioned to resist transverse shear equal to 2.5% of the axial force in the column.
VI) The minimum flat width should not be less than three times the nominal diameter of the end connector.
VII) The thickness of the lacing flat for single lacing system should be less than 1/40 of its effective length and for double lacing system it should be less than 1/60 of its effective length.
VIII) The slenderness ratio of the lacing bar should be less than 145.
X) The effective length of lacing bar is the length between the inner end rivets/bolts for a single lacing system and 0.7 times this distance for a double lacing system.
Purlins
Purlins are designed as continuous beams and are supported by rafters.
Principal rafter is the top chord member of truss and is subjected to compressive forces from loads transferred by purlins at the nodes.
The rafters act as simply supported beams between the purlins.
Purlins are designed as continuous beam and design bending moment is WL/10
As per IS 800: 2007, Clause No. 3.8,
Slenderness ratio of steel sections is limited as per the following:
:
Member | Maximum Effective Slenderness ratio |
Pure Compression Member | 180 |
Pure tension Member | 400 |
Tension Member subjected to reversal of stress due to loads other than wind and earthquake. | 180 |
Tension Member subjected to reversal of stress due to wind or earthquake load. | 350 |
A member subjected to compression forces resulting from wind or earthquake forces provided that deformation of such member does not affect the stress in any part of structure. | 250 |
Compression flange of beam against lateral torsional buckling | 300 |
As per IS code effective length for different end conditions:
| Degree of end restraint of compression member | Recommended value of effective length |
| 1. Effectively held in position and restrained against rotation at both ends | 0.65 L |
| 2. Effectively held in position at both ends restrained against rotation at one end | 0.80 L |
| 3. Effectively held in positions at both ends, but not restrained against rotation | 1.00 L |
| 4. Effectively held in position and restrained against rotation at one end, and at the other end restrained against rotation but not held in position | 1.20 L |
5. Effectively held in positions and restrained against rotation at one end and at the other end partially restrained against rotation but not held in position. | 1.50 L |
| 6. Effectively held in position at one end but not restrained against rotation, and at the other end restrained against rotation but not held in position | 2.00 L |
| 7. Effectively held in position and restrained at one end but not held in position nor restrained against rotation at the end | 2.00 L |
⇒ Due to direct load P, all bolts are subjected to shearing and bearing.
⇒ Due to bending moment = P.e., bolts above Neutral axis (NA) are subjected to tension and bolts below NA are useless in resisting compression. Compressive stresses are resisted by
1. flange of I-section, channel section, angle section etc. and
2. the portion of bracket below neutral axis by pressing against each other.
Assumptions in the design of riveted joints:
The friction among the plates is neglected.
Shear stress across a cross-section of a rivet is uniform.
The bearing stress distribution on the plate cross-section between rivet holes is uniform.
All rivets within a riveting group subjected to a direct load passing through their CG share the load equally.
Rivet shanks and after driving, fill the rivet holes completely.
The tensile stress is uniform in the section of metal between the rivets.
As per IS 800: 2007, clause 10.5.2.3 the size of fillet welds shall not be less than 3 mm.
The Value of Effective throat thickness either depends upon K values which depends on the angle between fusion faces or depends upon the size of the weld.
Throat Thickness (Tt) = K × Size of the weld
The K values vary as mentioned in the table below
Angle between fusion faces (in degrees) | 60 to 90 | 91 to 100 | 101 to 106 | 107 to 113 | 114 to 120 |
K | 0.7 | 0.65 | 0.6 | 0.55 | 0.5 |
