Design of steel structures (Limit State Method)

Design of Steel Structures (Limit State Design)

Disclaimer:

This document does not claim any originality and cannot be used as a substitute for prescribed textbooks. I would like to acknowledge various sources like freely available materials from internet particularly NPTEL/ SWAYAM course material from which the lecture note was prepared. The ownership of the information lies with the respective authors or institutions. Further, this document is not intended to be used for commercial purpose and the BlogSpot owner is not accountable for any issues, legal or otherwise, arising out of use of this document.

This open resource is a collection of academic course under graduation program for B.Tech (Civil Engineering) as per the syllabus of Dr. B.A.T University, Lonere, Raigad (m.s), India prepared by Dr. Mohd. Zameeruddin, Assistant Professor, at MGM's College of Engineering, Nanded for use in out-of-class activity. The course content covers both theoretical and analytical studies. There are six modules as part of this document, and each deals with an aspect related to the design of steel structures. 

Module 1: Introduction and design of connections

Module 2: Design of Tension Member

Module 3: Design of Compression Member

Module 4: Design of Beams

Module 5: Design of Plate and Gantry Girders

Module 6: Design of Roof Truss

Unit 1: Introduction and design of connections   

Performance Expected from a Structure

1. Stresses must be within limit
2. Deflection must be within limit
3. Structure must be stable
4. Structure must have adequate life
5. Structure must not vibrate dangerously
6. Structure must be easy to maintain
7. Structure must have pleasing appearance
8. Structure must be easy to construct
9.  Structure must have enough ductility

What are Steel Structures?

The various structures which come under the realm of civil engineering such as; buildings, bridges, dams, towers are constructed with a variety of materials such as concrete, steel, masonry, timber, cast iron, and plastic. The structures which are constructed using structural steel are called as steel structures such as; steel buildings (ware houses, factories, super market and offices), steel bridges, and steel towers [K. S. Sai Ram, Pearson 2010]

 

What does Structural Steel Consists of ?

The various structural elements in a steel structure may be classified as;

• Tension Member (Carrying Tensile Force) 
• Compression Member (Carrying Compressive Force)
• Beams and Girders (Carrying Flexural Forces)
• Beam-Column (Combined action of Bending and Bearing)
• Column bases and caps (Combined action of Compression and Flexure)
• Brackets (Shear, Twist and Bending)
• Connections (Pinned, Semi-rigid, and Rigid)
• Trusses (Axial Compression/Tension, Skeletal Geometry)

Advantages & disadvantages of steel as structural steel

          (reference Design of steel structures (LSM) by SK Duggal, McGraw hill publication)

ADVANTAGES

1. Steel members have high strength per unit weight. Therefore, a steel member of a small section which has little self-weight is able to resist heavy loads. The high strength of steel results in smaller sections to be used & fewer columns in buildings.
2. Steel being a ductile material hence does not fail suddenly, but gives visible evidence of impending failure by large deflections. 
3. Structural steels are tough, i.e. they have both strength and ductility. Thus, steel members subjected to large deformations during fabrication and erection will not fracture. 
4. Steel may be bent, hammered, sheared or even the bolt holes may be punched without any visible damage.
5. Properly maintained steel structures have a long design life.
6. Additions and alterations can be made easily to the steel structures.
7. They can be erected at a faster rate.
8. Steel can be reused after a structure is disassembled.
9. Steel is the ultimate recyclable material.

DISADVANTAGES           

1. Steel structures, when placed in exposed conditions, are subjected to corrosion, hence requires anti-corrosive treatment which increases cost for maintenance.
2. Steel structures need fireproof treatment which increases cost for maintenance.
3. Steel is an excellent heat conductor and therefore steel members may transfer enough heat from a burning section or a room of a building to ignite materials with which they are in contact in the adjoining room.
4.  Fatigue of steel is one of the major drawbacks. Fatigue involves a reduction in the strength when steel is subjected to a large number of variations in tensile stress.
5. At the places of stress concentrations in the steel sections, under certain conditions, the steel may lose its ductility.

Structural Steel

Structural Steel is obtained by adding small quantities of carbon during the manufacturing process of Iron. As on today, there are variety of steel produced by adding appropriate quantities of alloying elements such as Carbon (C), Manganese (Mn), Silicon (Si), Chromium (Cr), Nickel (Ni) and Molybdenum (Mo) to suit the needs of wide range of application. Table 1 shows the chemical composition of structural steel.

Table 1: Chemical Composition of Structural Steel

[K. S. Sai Ram, Pearson 2010]

Grade Designation	Quality	Ladle analysis, Percentage, Max					Carbon Equivalent, Max
		C	Mn	S	P	Si
E165	-	0.25	1.25	0.045	0.045	-	-
E250	A	0.23	1.50	0.045	0.045	0.40	0.42
E250	B	0.22	1.50	0.045	0.045	0.40	0.41
E250	C	0.20	1.50	0.04	0.04	0.40	0.39
E300	-	0.20	1.30	0.045	0.045	0.45	0.4
E350	-	0.20	1.50	0.045	0.045	0.45	0.42
E410	-	0.20	1.60	0.045	0.045	0.45	0.44
E450	D	0.22	1.60	0.045	0.045	0.45	0.46
E450	E	0.22	1.80	0.045	0.045	0.45	0.45

The Bureau of Indian Standards (BIS) standardized structural steel to be used in steel structures. IS 2062:2006  provided details of hot-rolled low, medium and high tensile structural steel. This standard covers the requirement of micro-alloyed plates, strips, shape and sections (Angles, Tees, Beams, and Channels), Flats and Bars of structural work. These steels are suitable for welded, bolted and riveted structures and for general engineering purposes.IS 2062:2006 has recommended nine grades of steel designated on the basis of their yield strength as tabulated in Table 2

  

Table 2: Different Grades of Structural Steel

Grade Designation	Quality	Tensile Strength (MPa)	Yield Strength (MPa)			Percentage Elongation
			t < 20	20 < t < 40	t > 40
E165	-	290	165	165	165	23
E250	A	410	250	240	230	23
E250	B	410	250	240	230	23
E250	C	410	250	240	230	23
E300	-	440	300	290	280	22
E350	-	490	350	330	320	22
E410	-	540	410	390	380	20
E450	D	570	450	430	420	20
E450	E	590	450	430	420	20

Where t = thickness of the element. Steel of quality A. B, and C are generally suitable for welding process. Weldability increases from quality A to C

Stress-Strain Relationship of Steel

The response of structural steel can be traced through stress-strain plot as shown in Figure 1.

  Fig.1. Stress-strain curves for structural steel in tension (ML Gambhir, 2013)

A Structural member exhibits an elastic range (a-b); plastic range (b-e). In the plastic range the member shows large extension for constant load (b-c). On further loading the material exhibits a small increase in load and associated elongation (strain hardening;c-d). After reaching ultimate load the loading decreases with increase in elongation up to rupture.

        For  sharp yielding structural steel, yield strength fy is the stress corresponding to position AB of the stress-strain curve. In continuously yielding structural steel, yield strength fy is the stress corresponding 0.2% strain obtained by drawing a line parallel to OA of the stress-strain curve. the stress corresponding to top-most point C on the stress-strain curve is the ultimate strength fu of the steel. The ductility of the steel (deformation without fracture) is measured using empirical relation 5.65 sqrt (So). So is the cross-sectional area of bar in unstressed state. 

Product of Structural Steel (Indian)

A variety of structural steel products are manufactured by steel plants in India. These products are made in different shapes and sizes to enable the structural engineer to select suitable section to satisfy design requirements. These section are classified based on manufacturing process in two categories as Hot-rolled sections and Cold-formed sections.

Hot-Rolled Sections

Hot-rolled sections are produced in steel plants from steel billets by passing through series of rollers. The various products made using this process are plates, strips, flats, bars, shape and sections (Angles, Tees, Beams, Channels)and etc. They are classified by the bureau of Indian Standard as follows;

Beams:

1. Indian Standard Column Sections (ISSC)
2. Indian Standard Junior Beams (ISJB)
3. Indian Standard Light Weight Beams (ISLB)
4. Indian Standard Medium Weight Beams (ISMB)
5. Indian Standard Heavy Weight Beams (ISHB)
6. Indian Standard Wide Flange Beams (ISWB)

These sections are designated as; for example ISJB200, ISLB200, ISMB200, ISHB200 and ISWB200 where 200 is the depth of the section in mm. The properties of these section are published in standard book IS 808: 1989

Channels:

 

1. Indian Standard Junior Channel (ISJC)
2. Indian Standard Light Weight Channels (ISLC)
3. Indian Standard Medium Weight Channels (ISMC)
4. Indian Standard Medium Weight Parallel Flange Channels (ISMCP)

These sections are designated as; for example ISJC100, ISLC100, ISMC100, ISMCP100  where 100 is the depth of the section in mm. The properties of these section are published in standard book IS 808: 1989

Tees: 

1. Indian Standard Rolled Normal Tee Bars (ISNT)
2. Indian Standard Rolled Deep Legged Tee Bars (ISDT)
3. Indian Standard Slit Light Weight Tee Bars (ISLT)
4. Indian Standard Slit Medium Weight Tee Bars (ISMT)
5. Indian Standard Slit Tee Bars from H Sections (ISHT)

These are designated as, ISNT100, ISDT100, ISLT150, ISMT 200, ISMT150, ISHT300 where the numerical value indicates the depth of the section in mm. the properties of these section are given in standard book IS 1173: 1978

Angles:

Indian Standard Equal/ Unequal angle (ISA) abbreviated as ISA. For example ISA 150mm x 150mm x 12mm, where 150 and 150 are the lengths of the legs in mm and 12 mm is the thickness of the member. The properties of these section are published in standard book IS 808: 1989

Tubular Sections:

These are designated by their nominal bore and classified as light, medium and heavy depending on the wall thickness. They are further graded as YSt 210, YSt 240 and YSt 310 depending on the yield stress of the material. The numerical value represents yield strength of material. The properties of these sections are published in standard book IS 1161: 1998

Rectangular/Square Hollow Sections:

These are designated by their outside dimension and thickness. For example 60 x 40 x 2.9 HF RHS right hand side represent the dimension of section as 60mm is the depth, 40mm is the breadth and 2.9 mm in thickness, and RHS for Rectangular  Hollow Section. They are further graded as YSt 210, YSt 240 and YSt 310 depending on the yield stress of the material. The numerical value represents yield strength of material. The properties of these sections are published in standard book IS 4923: 1997

Plates, Sheets, Strips and Flats: 

Plates are designated as ISPL followed by figures Length x Width x Thickness in mm, for example 600 x 450 x 12. Sheets are designated as IISH followed by figures Length x Width x Thickness in mm, for example 450 x 450 x 10. Strips are designated as ISST followed by figures denoting Width x Thickness in mm, for example 400 x 8 mm. Flats are designated by the width followed by letters ISF and the thickness in mm, 400ISF8. The properties of these sections are published in standard book IS 1730:1989

Cold-Formed Light Gauge Sections
The intention of reducing the weight of structures design engineers has focused of light weight section. These sections are produced from steel strips of 8mm thickness or less. The mass production of these sections are done with the help of press shop. They are available in the form of equal angles, unequal angles, channels, hats sections, and z section. these sections are designated by numbers denoting depth (mm) x width (mm) x thickness (mm).  The properties of these sections are published in standard book IS 811:1987

Standards, Codes and Specification
The design practices is based on specification and stipulation of relevant codes. In India, several development and experimentation has been taken place for improving the material property of structural steel. Bureau of Indian standard has taken major effort in this process by publication of IS 800:1984 Code of Practice for General Construction in Steel.The earlier version of IS 800: 1984 was based on allowable Stress Design (Working), which has been revised incorporating the Load and Resistance Factor Design (LRFD) and Limit State Method (LSM) in 2007.

Structural Loads
A structure is designed to carry certain loads so as to serve the intended purpose. The primarily load considered are; Dead loads, Imposed(Live) loads, Wind loads, Seismic loads, Snow load, Erection load, and effects of temperature etc.

1. Dead Loads

Dead loads are permanent or stationary loads which are transferred to structure throughout the life span. Dead load is primarily due to self weight of structural members, permanent partition walls, fixed permanent equipment's and weight of different materials IS 875 Part 1.

2. Live Loads

Live loads are either movable or moving loads with out any acceleration or impact. There are assumed to be produced by the intended use or occupancy of the building including weights of movable partitions or furniture etc IS 875 Part 2. 

 3. Snow Loads

 The amount of snow load on a roof structure is dependent on a variety of factors IS 875 Part 4;

1.            Roof geometry, 
2.            Size of the structure, 
3.            Insulation of the structure, 
4.            Wind frequency, 
5.            Snow duration, and 
6.            Geographical location of the structure.

 4. Impact Loads
 Impact load is caused by vibration or impact or acceleration. Thus, impact load is equal to imposed load incremented by some percentage called impact factor or impact allowance depending upon the intensity of impact.

5. Earthquake Loads (Seismic Loads)

Earthquake loads are horizontal loads caused by the earthquake and shall be computed in accordance with IS 1893. For monolithic reinforced concrete structures located in the seismic zone 2, and 3 without more than 5 storey high and importance factor less than 1, the seismic forces are not critical IS 1893 Part 1 (2016).

6. Wind Loads

Wind load is primarily horizontal load caused by the movement of air relative to earth. Wind load is required to be considered in design especially when the heath of the building exceeds two times the dimensions transverse to the exposed wind surface. The amount of wind load is dependent on the following IS 875 Part 3;

1. Geographical location
2. The height of structure
3. Type of surrounding physical environment
4. The shape of structure Size of the building

Types of Member Force
1. Tension Forces

2. Compression forces 

3. Bending/ Flexural Forces

Design Philosophies 

[Arijit Guha (2016), The Bridge and Structural Engineer, 46(2): 57-65]

1. Working Stress Method
With the development of linear elastic theories in 19th century it became possible to understand the stress-strain behavior of wrought  iron and mild steel  accurately. With this theories designers are able to analyze indeterminate structures. The response quantities are yield stress, ultimate stress, bending stresses, and shear stresses. The first attainment of yield stress of steel was taken s onset of failure. The limitation due to non-linearity and buckling are neglected. 
The criteria for the design are expressed a; 

factual  ≤ fallowable

Allowable stress (Working stress) = Yield stress/ Factor of safety 

The allowable stress is defined in terms of factor of safety which defines acceptable limits for overload and other unknown factors which could not be tolerated by the structure. This factor of safety has implied rigidity to design irrespective to the frequency and magnitude of loading.The structure is design for various combination of loading. The value of factor of safety in many of the loading cases is taken to be 1.67. Designing the structure for same factor of safety in combination resulted in uneconomical design. A typical set of load combination are;

Stresses due to Dead load + Live load < Allowable stress

Stress due to Dead load + Wind load < Allowable stress

Stresses due to Dead load + Live load + Wind load < 1.33 x Allowable stress

In practice there are severe limitations to this approach. These are consequences of material non-linearity, post-buckled state of elements, redistribution of loads.

2. Limit State Method
To overcome the limitations of working stress method, limit state method was proposed using the plastic range of material for the design of structural members and load factor to account for variability in loading configurations. This rational factor of safety in different structural performance enables to use steel efficiently and economically in different structural systems to withstand tension, compression, flexural and torsional loads.
 
         Limit state method takes into account of variance by defining limit states addressing strength and serviceability. In LSM a structure or part of it is considered unfit for use when it exceeds the limit states, beyond which it infringes one of the criteria governing its performance or use. The limit states are classified as strength based limit state and serviceability based limit state. Strength based limit state are defined by yielding, plastic strength, fatigue, buckling etc. Serviceability limit state are defined by deflection, vibration, drift, etc.

            In LSM, the factored loads, in different loading combinations are applied to the structure to determine the load effects. The later are compared with the design strength of individual element.
Let;

S* ≤ R*

S* is the calculated load effect on the element (Bending moment, Shear force, Tension, Compression, Torsion, etc)
R* is the calculated factored resistance of the element being checked, and is function of the nominal size of the material yield strength.


Numerical 1
An industrial building is to be designed in Aurangabad. Compute the design wind speed and wind pressure at a height of 15m. the building has maximum dimension of 30m.
Answer:

For Aurangabad the basic wind speed Vb = 39 m/s (Appendix A: IS 875 [Part 4])
Design Life Span of Industrial Building is assumed to be 50 Years k1 =1.0 
The terrain is in industrial area and hence it belongs to category 3 and Class B. Hence from Table 2 (IS 875: Part 4) k2 = 0.97 for height 15 m. The ground is assumed to be plain and uniform k3=1. 

Design Wind Speed; Vz = k1 x k2 x k3 x Vb    

                                     Vz = 1.0 x 0.97 x 1.0 x 39

                     Vz = 37.83 m/s

Design Wind Pressure; Pz = 0.6 x (Vb)^2   

                                     Pz = 858.66 MPa

Numerical 2
The plan and elevation of a three storey school building is shown in figure given below. The building is located in Aurangabad (Zone III). The type of soil encountered is medium soil and it is proposed to to design the building with special moment resisting frames . The intensity of dead load is 10 kN/m^2 and the floors are subjected to live load of 3kN/m^2. Determine the lateral loads on the various floor levels of the structure by static analysis. 

Answer:
Dead Load on Structure
                   = Intensity of loading x Plan area
                   = 10 x 3 x 3 = 90 kN
Live Load on Structure
                   = Intensity of loading x Plan area
                   = 3 x 3 x 3 = 27 kN
Seismic Load of one floor: 
                    = Dead Load + 0.25 (Live Load) [ as per Table 8 of IS 1893(Part 1):2002]
                    = 90 + 0.25*27
                    = 96.75 kN
 Total Seismic Load = 5 x 96.75 = 483.75
Zone factor (z) = 0.16 [as per Table 2 of IS 1893(Part 1):2002]
Importance Factor (I) = 1.0 [as per Table 6 of IS 1893(Part 1):2002]
Response Reduction factor (R) = 5 [SMRF as per Table 7 of IS 1893(Part 1):2002]
Base Shear coefficient (Ah) = (ZI/2R)*(Sa/g) [as per clause 6.4.2 of IS 1893(Part 1):2002]
(Sa/g) is read from Figure 2 of IS 1893(Part 1):2002 for medium soil type for natural period obtained from the relation Ta = 0.075h^0.75 = 0.075(15)^0.75 = 0.571  worked out to be 2.5.
                                          Ah = (ZI/2R)*(Sa/g) = (0.16 x1/2 x 5) x 2.5 = 0.04
Base Shear (Vb) = Ah x Total seismic weight all floors
                   = 0.04 x 483.75 = 19.35 kN
Lateral load on each floor (Fi) =  Vb x [(wihi^2)/ summation of (wihi^2)]

     Floor           height (m)         Vb (kN)            wihi^2                    Fi (kN)

         1                    3                    19.35               870.75          0.018 x 19.35 = 0.348

         2                    6                    19.35             3483.00          0.072 x 19.35 = 1.393

         3                    9                    19.35             7836.75          0.163 x 19.35 = 3.154

         4                   12                   19.35           13932.00          0.291 x 19.35 = 5.629

         5                   15                   19.35           21768.75          0.454 x 19.35 = 8.784

                          Total                 483.75           47891.30

Numerical 3











Types of Structural Steel 

Advantages & disadvantages of bolted connections
(Reference Design of steel structures-I by Dr. RV Gehlot, Scientific Publishers, India)

ADVANTAGES

1. The process is silent, compare to the riveted connection where hammering is done. 
2.  There is no risk of fire, as compared to red-hot riveting and welding.  
3.  Less time consuming in compared to the riveted connection.
4. The overall cost of bolted construction is cheaper than that of riveted construction because of the reduced labour and equipment costs and a smaller number of bolts required for resisting the same load.
5.   It facilitates the erection because of the ease with which these connections can be done.

DISADVANTAGES

1.  If bolted connections become loose, their strength reduces considerably.
2. The unfinished bolts are not uniform in diameter and they have less strength.
3.  The bolted connection has less strength when they are subjected to axial tension because area at the root of the thread is less. 
4. Generally, the diameter of the hole is kept 2 mm more than the nominal diameter of the black bolt. The bolt does not fill the hole and there remains a clearance in bolted connections.
5. Cost of material is high, about double that of rivets.