This document discusses the design of compression members in steel structures. It begins by defining compression members as members subjected to compressive stresses, such as columns, struts, and compression flanges. It notes that compression members are more prone to buckling than tension members. The document then discusses factors that influence the buckling strength of compression members, such as the member's length, cross-sectional properties, end conditions, and bracing. It also discusses eccentric loading of columns and the various sections that can be used or built up for compression members.
Designing a Concrete Beam Using the New AS3600:2018 - Webinar Slides - ClearC...ClearCalcs
The 2018 revision of the AS3600 Concrete standard includes major revisions for areas including phi factors, shear, deflection, rectangular stress block, and shrinkage/creep.
In this webinar, ClearCalcs lead engineering developer Brooks Smith discusses some of these key changes, and runs through the design process for a concrete beam design before demonstrating a few worked examples using AS3600:2018 in the newly released rectangular concrete beam calculator on ClearCalcs.com.
Watch the recorded webinar: https://vimeo.com/295532300
Explore all of our concrete, timber, and steel calculations at clearcalcs.com.
Abstract (Dutch)
Samengestelde betonnen liggers vervaardigd van prefab voorgespannen- en/of gewapende elementen zijn zeer populair in de huidige praktijk van de civiele techniek. Twee betonnen, samengestelde delen van de ligger worden gestort op verschillende tijdstippen. Verschillende elasticiteitsmoduli, opeenvolgende belastingaanbrenging, en verschillend krimp en kruip veroorzaken een herverdeling van de normaalspanning en ongelijke rekken en spanningen in twee aansluitende vezels in het aansluitvlak.
Dit seminar richt zich op de berekening volgens de EN 1992-1-1 en EN 1992-2. De aannames met betrekking tot de berekening en de controle van de gewapende en/of voorgespannen samengestelde liggers en doorsnedes zal worden toegelicht.
Ook wordt er ingegaan op:
• De spanning/rek respons van de doorsnede belast door normaalkracht en buigende momenten,
• De principes van het gebruik van de “initiële toestand” in berekeningen van de uiterste grenstoestand en de bruikbaarheidsgrenstoestand,
• De controle van dwarskracht en wringing,
• De interactie tussen alle snedekrachten,
• De principes van de controles van de spanningbeperking,
• De achtergrond van de scheurwijdtecontrole
Speciale aandacht zal er worden gegeven aan de berekening van de schuifspanning in het aansluitvlak, en de beschouwing van de invloed van de verschillende leeftijd van de betonnen delen met betrekking tot de schuifspanningen. Een alternatieve berekeningsmethode ten opzichte van de Eurocode 2 zal worden voorgesteld en worden getest.
De praktische voorbeelden volgens de Eurocode 2 zullen worden uitgevoerd met behulp van de IDEA StatiCa software.
Design and Detailing of RC Deep beams as per IS 456-2000VVIETCIVIL
Visit : https://teacherinneed.wordpress.com/
1. DEEP BEAM DEFINITION - IS 456
2. DEEP BEAM APPLICATION
3. DEEP BEAM TYPES
4. BEHAVIOUR OF DEEP BEAMS
5. LEVER ARM
6. COMPRESSIVE FORCE PATH CONCEPT
7. ARCH AND TIE ACTION
8. DEEP BEAM BEHAVIOUR AT ULTIMATE LIMIT STATE
9. REBAR DETAILING
10. EXAMPLE 1 – SIMPLY SUPPORTED DEEP BEAM
11. EXAMPLE 2 – SIMPLY SUPPORTED DEEP BEAM; M20, FE415
12. EXAMPLE 3: FIXED ENDS AND CONTINUOUS DEEP BEAM
13. EXAMPLE 4 : FIXED ENDS AND CONTINUOUS DEEP BEAM
Designing a Concrete Beam Using the New AS3600:2018 - Webinar Slides - ClearC...ClearCalcs
The 2018 revision of the AS3600 Concrete standard includes major revisions for areas including phi factors, shear, deflection, rectangular stress block, and shrinkage/creep.
In this webinar, ClearCalcs lead engineering developer Brooks Smith discusses some of these key changes, and runs through the design process for a concrete beam design before demonstrating a few worked examples using AS3600:2018 in the newly released rectangular concrete beam calculator on ClearCalcs.com.
Watch the recorded webinar: https://vimeo.com/295532300
Explore all of our concrete, timber, and steel calculations at clearcalcs.com.
Abstract (Dutch)
Samengestelde betonnen liggers vervaardigd van prefab voorgespannen- en/of gewapende elementen zijn zeer populair in de huidige praktijk van de civiele techniek. Twee betonnen, samengestelde delen van de ligger worden gestort op verschillende tijdstippen. Verschillende elasticiteitsmoduli, opeenvolgende belastingaanbrenging, en verschillend krimp en kruip veroorzaken een herverdeling van de normaalspanning en ongelijke rekken en spanningen in twee aansluitende vezels in het aansluitvlak.
Dit seminar richt zich op de berekening volgens de EN 1992-1-1 en EN 1992-2. De aannames met betrekking tot de berekening en de controle van de gewapende en/of voorgespannen samengestelde liggers en doorsnedes zal worden toegelicht.
Ook wordt er ingegaan op:
• De spanning/rek respons van de doorsnede belast door normaalkracht en buigende momenten,
• De principes van het gebruik van de “initiële toestand” in berekeningen van de uiterste grenstoestand en de bruikbaarheidsgrenstoestand,
• De controle van dwarskracht en wringing,
• De interactie tussen alle snedekrachten,
• De principes van de controles van de spanningbeperking,
• De achtergrond van de scheurwijdtecontrole
Speciale aandacht zal er worden gegeven aan de berekening van de schuifspanning in het aansluitvlak, en de beschouwing van de invloed van de verschillende leeftijd van de betonnen delen met betrekking tot de schuifspanningen. Een alternatieve berekeningsmethode ten opzichte van de Eurocode 2 zal worden voorgesteld en worden getest.
De praktische voorbeelden volgens de Eurocode 2 zullen worden uitgevoerd met behulp van de IDEA StatiCa software.
Design and Detailing of RC Deep beams as per IS 456-2000VVIETCIVIL
Visit : https://teacherinneed.wordpress.com/
1. DEEP BEAM DEFINITION - IS 456
2. DEEP BEAM APPLICATION
3. DEEP BEAM TYPES
4. BEHAVIOUR OF DEEP BEAMS
5. LEVER ARM
6. COMPRESSIVE FORCE PATH CONCEPT
7. ARCH AND TIE ACTION
8. DEEP BEAM BEHAVIOUR AT ULTIMATE LIMIT STATE
9. REBAR DETAILING
10. EXAMPLE 1 – SIMPLY SUPPORTED DEEP BEAM
11. EXAMPLE 2 – SIMPLY SUPPORTED DEEP BEAM; M20, FE415
12. EXAMPLE 3: FIXED ENDS AND CONTINUOUS DEEP BEAM
13. EXAMPLE 4 : FIXED ENDS AND CONTINUOUS DEEP BEAM
Design of steel structure as per is 800(2007)ahsanrabbani
It does not offer resistance against rotation and also termed as a hinged or pinned connections.
It transfers only axial or shear forces and it is not designed for moment
It is generally connected by single bolt/rivet and therefore full rotation is allowed
information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,
Experimental study on strength and flexural behaviour of reinforced concrete ...IOSR Journals
Abstract: Strength and flexural behaviour of reinforced concrete beams using deflected structural steel
reinforcement and the conventional steel reinforcement are conducted in this study. The reinforcement quantity
of both categories was approximately equalised. Mild steel flats with minimum thickness and corresponding
width are deflected to possible extent in a parabolic shape and semi-circular shape are fabricated and used as
deflected structural steel reinforcement in one part, whereas the fabrication of ribbed tar steel circular bars as
conventional reinforcement on the another part of the experiment for comparison in the concrete beams. All the
beams had same dimensions and same proportions of designed mix concrete, were tested under two point
loading system. As the result of experiments, it is found that the inverted catenary flats and their ties, transfers
the load through arch action of steel from loading points towards the supports before reaching the bottom
fibre at the centre of the beam as intended earlier. Thereby the load carrying capacity and the ductility ratio
has being increased in deflected structural steel reinforced beams when compared with ribbed tar steel
reinforced concrete beams, it is also observed that the failure mode (collapse pattern)is safer.
Keywords --Arch profile, Conventional steel reinforcement, Cracks, Collapse, Deflected structural steel,
Ductility ratio.
International Journal of Engineering and Science Invention (IJESI) inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
Design of steel structure as per is 800(2007)ahsanrabbani
It does not offer resistance against rotation and also termed as a hinged or pinned connections.
It transfers only axial or shear forces and it is not designed for moment
It is generally connected by single bolt/rivet and therefore full rotation is allowed
information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,
Experimental study on strength and flexural behaviour of reinforced concrete ...IOSR Journals
Abstract: Strength and flexural behaviour of reinforced concrete beams using deflected structural steel
reinforcement and the conventional steel reinforcement are conducted in this study. The reinforcement quantity
of both categories was approximately equalised. Mild steel flats with minimum thickness and corresponding
width are deflected to possible extent in a parabolic shape and semi-circular shape are fabricated and used as
deflected structural steel reinforcement in one part, whereas the fabrication of ribbed tar steel circular bars as
conventional reinforcement on the another part of the experiment for comparison in the concrete beams. All the
beams had same dimensions and same proportions of designed mix concrete, were tested under two point
loading system. As the result of experiments, it is found that the inverted catenary flats and their ties, transfers
the load through arch action of steel from loading points towards the supports before reaching the bottom
fibre at the centre of the beam as intended earlier. Thereby the load carrying capacity and the ductility ratio
has being increased in deflected structural steel reinforced beams when compared with ribbed tar steel
reinforced concrete beams, it is also observed that the failure mode (collapse pattern)is safer.
Keywords --Arch profile, Conventional steel reinforcement, Cracks, Collapse, Deflected structural steel,
Ductility ratio.
International Journal of Engineering and Science Invention (IJESI) inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
Effect of creep on composite steel concrete sectionKamel Farid
Creep and Shrinkage are inelastic and time-varying strains.
For Steel-Concrete Composite beam creep and shrinkage are highly associated with concrete.
Simple approach depending on modular ratio has been adopted to compute the elastic section properties instead of the theoretically complex calculations of creep.
What are methods of steel structure designnajeeb muhamed
There are three different methods for design of steel structure, i.e. simple design, continuous design and semi-continuous steel design.
Joints in structures have been assumed to behave as either pinned or rigid to render design calculations manageable.
In simple design the joints are idealised as perfect pins. Continuous design assumes that joints are rigid and that no relative rotation of connected members occurs whatever the applied moment.
The vast majority of designs carried out today make one of these two assumptions, but a more realistic alternative is now possible, which is known as semi-continuous design.
International Journal of Computational Engineering Research(IJCER) ijceronline
nternational Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
The Internet of Things (IoT) is a revolutionary concept that connects everyday objects and devices to the internet, enabling them to communicate, collect, and exchange data. Imagine a world where your refrigerator notifies you when you’re running low on groceries, or streetlights adjust their brightness based on traffic patterns – that’s the power of IoT. In essence, IoT transforms ordinary objects into smart, interconnected devices, creating a network of endless possibilities.
Here is a blog on the role of electrical and electronics engineers in IOT. Let's dig in!!!!
For more such content visit: https://nttftrg.com/
RAT: Retrieval Augmented Thoughts Elicit Context-Aware Reasoning in Long-Hori...
05 compression members (1)
1. Civil Engineering Department – University of Lahore.
Design of Steel Structures
1
DESIGN OF COMPRESSION
MEMBERS
1/3
Department of Civil Engineering
The University of Lahore, Lahore
2. Civil Engineering Department – University of Lahore.
Design of Steel Structures
COMPRESSION MEMBERS
When a load tends to squeeze or shorten a
member, the stresses produced are said to be
compressive in nature and the member is
called a compression member (Figure 3.1).
2
Examples are struts (short compression
members without chances of buckling),
eccentrically loaded columns, top chords of
trusses, bracing members, compression
flanges of beams and members that are
subjected simultaneously to bending and
compressive loads.
P
P
3. Civil Engineering Department – University of Lahore.
Design of Steel Structures
There are two significant differences between the
behavior of tension and compression members, as
under:
1. The tensile loads tend to hold a member straight
even if the member is not initially in one line and is
subjected to simultaneous bending moments.
In contrast, the compressive loads tend to bend the
member out of the plane of the loads due to
imperfections, simultaneous bending moment or
even without all of these.
3
4. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Tests on majority of practical columns show that they
will fail at axial stresses well below the elastic limit of
the column material because of their tendency to buckle
(which is a sudden lateral bending due to a critical
compressive force).
For these reasons, the strength of compression members
is reduced in relation to the danger of buckling
depending on length of column, end conditions and
cross-sectional dimensions.
The longer a column becomes for the same cross-
section the greater is its tendency to buckle and the
smaller is the load it will support.
4
5. Civil Engineering Department – University of Lahore.
Design of Steel Structures
When the length of a compression member increases
relative to its cross-section, it may buckle at a lower load.
After buckling the load cannot be sustained and the load
capacity nearly approaches zero.
The condition of a column at its critical buckling load is
that of an unstable equilibrium as shown in Figure 3.2.
5
(a) Stable (b) Neutral (c) Unstable
Figure 3.2. Types of Equilibrium States.
6. Civil Engineering Department – University of Lahore.
Design of Steel Structures
In the first case, the restoring forces are greater than the
forces tending to upset the system.
Due to an infinitesimal small displacement consistent
with the boundary conditions or due to small
imperfection of a column, a moment is produced in a
column trying to bend it.
At the same time, due to stress in the material, restoring
forces are also developed to bring the column back to
its original shape.
If restoring force is greater than the upsetting moment,
the system is stable but if restoring force is lesser than
the upsetting moment, the system is unstable.
6
7. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Right at the transition point when restoring force is
exactly equal to the upsetting moment, we get neutral
equilibrium.
The force associated with this condition is the critical
or buckling load.
2. The presence of rivet or bolt holes in tension
members reduces the area available for resisting
loads; but in compression members the rivets or
bolts are assumed to fill the holes and the entire
gross area is available for resisting load.
7
8. Civil Engineering Department – University of Lahore.
Design of Steel Structures
CONCENTRICALLY AND ECCENTRICALLY
LOADED COLUMNS
The ideal type of load on a column is a concentric load
and the member subjected to this type of load is called
concentrically loaded column.
The load is distributed uniformly over the entire cross-
section with the center of gravity of the loads coinciding
with the center of gravity of the columns.
Due to load patterns, the live load on slabs and beams
may not be concentrically transferred to interior
columns.
8
9. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Similarly, the dead and live loads transferred to the
exterior columns are, generally, having large eccentricities,
as the center of gravity of the loads will usually fall well
on the inner side of the column.
In practice, majority of the columns are eccentrically
loaded compression members
Slight initial crookedness, eccentricity of loads, and
application of simultaneous transverse loads produce
significant bending moments as the product of high axial
loads (P) multiplied with the eccentricity, e.
This moment, P e, facilitates buckling and reduces the
load carrying capacity.
9
10. Civil Engineering Department – University of Lahore.
Design of Steel Structures
P
a) Initial
Crookedness
P
e
P
e
b) Eccentric Load
P
P
c)Simultaneous
Transverse Load
10
Eccentricity, e, may be relatively smaller, but the product
(P e) may be significantly larger.
11. Civil Engineering Department – University of Lahore.
Design of Steel Structures
11
Figure: Typical initial deflections of stiffened panels: (a) out-of-flatness of a
subpanel; (b) out-of-straightness of a stiffener; (c) stiffener camber deflection.
(IDM, 1987)
12. Civil Engineering Department – University of Lahore.
Design of Steel Structures
The AISC Code of Standard Practice specifies an acceptable
upper limit on the out-of-plumbness and initial crookedness
equal to the length of the member divided by 500.
(equal to 0.002, AISC C2-2b-3).
RESIDUAL STRESSES
Residual stresses are stresses that remain in a member after
it has been formed into a finished product.
These are always present in a member even without the
application of loads.
The magnitudes of these stresses are considerably high
and, in some cases, are comparable to the yield stresses
(refer to Figure 3.4).
12
13. Civil Engineering Department – University of Lahore.
Design of Steel Structures
83 to 93 MPa
80 to 95 MPa
(C)
(T)
a)Rolled Shapes
(C)
(T)
(C)
80 to 95 MPa
0.3Fy for A36
(T)
80 to 95 MPa
13
14. Civil Engineering Department – University of Lahore.
Design of Steel Structures
280 MPa (T)
84 MPa (C)
140 MPa (T)
140 MPa
(C)
240 MPa
(T)
140 MPa (C)
b)Welded Shapes
Weld
Weld
14
15. Civil Engineering Department – University of Lahore.
Design of Steel Structures
The causes of presence of residual stresses are as under:
1. Uneven cooling which occurs after hot rolling of
structural shapes produces thermal stresses, which are
permanently stored in members.
The thicker parts cool at the end, and try to shorten in
length. While doing so they produce compressive stresses
in the other parts of the section and tension in them.
Overall magnitude of this tension and compression remain
equal for equilibrium.
In I-shape sections, after hot rolling, the thick junction of
flange to web cools more slowly than the web and flange
tips.
15
16. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Consequently, compressive residual stress exists at flange
tips and at mid-depth of the web (the regions that cool
fastest), while tensile residual stress exists in the flange
and the web at the regions where they join.
2. Cold bending of members beyond their elastic
limit produce residual stresses and strains within the
members.
Similarly, during fabrication, if some member having
extra length is forced to fit between other members,
stresses are produced in the associated members.
3. Punching of holes and cutting operations during
fabrication also produce residual stresses.
16
17. Civil Engineering Department – University of Lahore.
Design of Steel Structures
4. Welding also produces the stresses due to uneven
cooling after welding.
Welded part will cool at the end inviting other parts to
contract with it.
This produces compressive stresses in parts away from
welds and tensile stresses in parts closer to welds.
SECTIONS USED FOR COLUMNS
Single angle, double angle, tee, channel, W-section, pipe,
square tubing, and rectangular tubing may be used as
columns.
Different combinations of these structural shapes may also
be employed for compression members to get built-up
sections as shown in Figure 3.5. 17
18. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Four Angles
Box Section
Two Inward
Channels Box
Section
Two Outward
Channels Box
Section
Built-Up
Box
W - Section
With Cover
Plates
Built-Up
ISection
Built-Up
Rectangular
Box
W And Channels
Built-Up Section Built-Up ISection
18
Figure 3.5: Built-up Section s for Compression Member
19. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Built-up sections are better for columns because the
slenderness ratios in various directions may be
controlled to get nearly equal values in all the
directions.
This makes the column economical as far as the
material cost is concerned. However, the joining and
labor cost is generally higher for built-up sections.
The total cost of these sections may become less for
greater lengths.
The joining of various elements of a built-up section is
usually performed by using lacing.
19
20. Civil Engineering Department – University of Lahore.
Design of Steel Structures
LIMITING SLENDERNESS RATIO
The slenderness ratio of compression members should
preferably not exceed 200 (AISC E2).
This means that in exceptional cases, the limit may be
exceeded.
20
B
A
C
Figure 3.6. Local Flange
Instability.
INSTABILITY OF COLUMNS
a) Local Instability
During local instability, the
individual parts or plate elements of
cross-section buckle without overall
buckling of the column.
21. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Width/thickness ratio of each part gives the slenderness
ratio ( = b/t), which controls the local buckling.
Local buckling should never be allowed to occur before
the overall buckling of the member except in few cases
like web of a plate girder.
An unstiffened element is a projecting piece with one
free edge parallel to the direction of the compressive
force.
The example is half flange AB in Figure 3.6.
A stiffened element is supported along the two edges
parallel to the direction of the force.
21
22. Civil Engineering Department – University of Lahore.
Design of Steel Structures
The example is web AC in the same figure.
For unstiffened flange of figure, b is equal to half width
of flange (bf / 2) and t is equal to tf. Hence, bf / 2tf ratio
is used to find .
For stiffened web, h is the width of web and tw is the
thickness of web and the corresponding value of or
b/t ratio is h / tw, which controls web local buckling.
Overall Instability
In case of overall instability, the column buckles as a
whole between the supports or the braces about an axis
whose corresponding slenderness ratio is bigger.
22
23. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Single angle sections may buckle about their weak axis
(z-axis, Figure 3.10).
Calculate Le / rz to check the slenderness ratio.
In general, all un-symmetric sections having non-zero
product moment of inertia (Ixy) have a weak axis different
from the y-axis.
Z
Z
Figure 3.10. Axis of Buckling For Single Angle Section.
23
30. Civil Engineering Department – University of Lahore.
Design of Steel Structures
a)Buckling about
major axis
b)Buckling about
minor axis
Figure 3.6- Buckling of a Column Without Intermediate Bracing
30
31. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Buckling
about
minor axis
Bracing to prevent
major axis buckling,
connected to stable
structures
Lx1
Lx2
31
33. Civil Engineering Department – University of Lahore.
Design of Steel Structures
UNSUPPORTED LENGTH
It is the length of column between two consecutive
supports or braces denoted by Lux or Luy in the x and y
directions, respectively.
A different value of unsupported length may exist in
different directions and must be used to calculate the
corresponding slenderness ratios.
To calculate unsupported length of a column in a
particular direction, only the corresponding supports
and braces are to be considered neglecting the bracing
preventing buckling in the other direction.
33
34. Civil Engineering Department – University of Lahore.
Design of Steel Structures
EFFECTIVE LENGTH OF COLUMN
The length of the column corresponding to one-half sine
wave of the buckled shape or the length between two
consecutive inflection points or supports after buckling
is called the effective length.
BUCKLING OF STEEL COLUMNS
Buckling is the sudden lateral bending produced by
axial loads due to initial imperfection, out-of-
straightness, initial curvature, or bending produced by
simultaneous bending moments.
34
35. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Chances of buckling are directly related with the
slenderness ratio KL/r and hence there are three
parameters affecting buckling.
1. Effective length factor (K), which depends on the
end conditions of the column.
2. Unbraced length of column (Lu), in strong
direction or in weak direction, whichever gives
more answer for KL/r.
3. Radius of gyration (r), which may be rx or ry
(strong and weak direction) for uniaxially or
biaxially symmetrical cross-sections and least
radius of gyration (rz) for un-symmetrical cross-
sections like angle sections.
35
36. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Following points must be remembered to find the critical
slenderness ratio:
a. Buckling will take place about a direction for
which the corresponding slenderness ratio is the
maximum.
b. For unbraced compression members consisting
of angle section, the total length and rz are used
in the calculation of KL/r ratio.
c. For steel braces, bracing is considered the most
effective if tension is produced in them due to
buckling.
36
37. Civil Engineering Department – University of Lahore.
Design of Steel Structures
d. Braces that provide resistance by bending are
less effective and braces having compression are
almost ineffective because of their small x-
sections and longer lengths.
e. The brace is considered effective if its other end
is connected to a stable structure, which is not
undergoing buckling simultaneously with the
braced member.
f. The braces are usually provided inclined to
main members of steel structures starting
from mid-spans to ends of the adjacent
columns.
37
38. Civil Engineering Department – University of Lahore.
Design of Steel Structures
g. Because bracing is most effective in tension, it
is usually provided on both sides to prevent
buckling on either side.
h. Bracing can be provided to prevent buckling
along weak axis. KL/r should be calculated by
using Ky, unbraced length along weak axis and ry.
i. Bracing can also be provided to prevent
buckling along the strong axis. KL/r in this case
should be calculated by using Kx, the unbraced
length along strong axis and rx.
j. The end condition of a particular unsupported
length of a column at an intermediate brace is
considered a hinge.
38
39. Civil Engineering Department – University of Lahore.
Design of Steel Structures
The reason is that the rotation becomes free at this point
and only the lateral movement is prevented.
EFFECTIVE LENGTH FACTOR (K)
This factor gives the ratio of length of half sine wave of
deflected shape after buckling to full-unsupported length
of column.
This depends upon the end conditions of the column and
the fact that whether sidesway is permitted or not.
Greater the K-value, greater is the effective length and
slenderness ratio and hence smaller is the buckling load.
39
40. Civil Engineering Department – University of Lahore.
Design of Steel Structures
K-value in case of no sidesway is between 0.5 and 1.0,
whereas, in case of appreciable sidesway, it is greater
than or equal to 1.0
Le = K Lu
40
SIDE SWAY
Any appreciable lateral or sideward movement of top of
a vertical column relative to its bottom is called
sidesway, sway or lateral drift.
If sidesway is possible, K-value increases by a greater
degree and column buckles at a lesser load.
41. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Sidesway in a frame takes place due to:-
a) Lengths of different columns are unequal.
b) When sections of columns have different cross-sectional
properties.
c) Loads are un-symmetrical.
d) Lateral loads are acting.
41
2I
I
I
(a) (b) (c) (d)
Figure 3.11. Causes of Sidesway in a Building Frame.
42. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Sidesway may be prevented in a frame by:
a. Providing shear or partition walls.
b. Fixing the top of frame with adjoining rigid
structures.
c. Provision of properly designed lift well or
shear walls in a building, which may act like
backbone of the structure reducing the
lateral deflections.
Shear wall is a structural wall that resists
shear forces resulting from the applied
transverse loads in its own plane and it
produces frame stability.
42
43. Civil Engineering Department – University of Lahore.
Design of Steel Structures
d. Provision of lateral bracing, which may be of
following two types:
i. Diagonal bracing, and
ii. Longitudinal bracing.
Unbraced frame is defined as the one in which the
resistance to lateral load is provided by the
bending resistance of frame members and their
connections without any additional bracing.
43
44. Civil Engineering Department – University of Lahore.
Design of Steel Structures
K-Factor for Columns Having Well Defined
End Conditions
Theoretical K=1.0
Practical K = 1.0
No Sidesway
Theoretical K = 0.5
Practical K = 0.65
No Sidesway
Inflection
Points
Le = L
Le = KL
44
Check the K-value for various end condition at Page 103
on Refernce-1 (LRFD Steel Design Aids)
45. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Theoretical K=2.0
Practical K = 2.10
Sidesway Present
Theoretical K=2.0
Practical K = 2.0
Sidesway Present
Le = KL
Theoretical K = 0.7
Practical K = 0.8
No Sidesway
Theoretical K=1.0
Practical K = 1.2
Sidesway Present
Le = KL
Le = KL
45
46. Civil Engineering Department – University of Lahore.
Design of Steel Structures
46
Simple or hinge Connection
Moment or Fix Connection
47. Civil Engineering Department – University of Lahore.
Design of Steel Structures
PARTIALLY RESTRAINED COLUMNS
Consider the example of column AB shown in Figure 3.13.
The ends are not free to rotate and are also not perfectly
fixed. Instead these ends are partially fixed with the fixity
determined by the ratio of relative flexural stiffness of
columns meeting at a joint to the flexural stiffness of
beams meeting at that joint.
This ratio is denoted by G or and is determined for each
end of the columns using following expression.
47
48. Civil Engineering Department – University of Lahore.
Design of Steel Structures
or G at each end =
EI of columns
EI of beams
A
B
B
GB or B
A
GA or A
Columns
Beams
Part-X
Column AB of Part-X
Figure 3.13. Partially restrained Columns
48
49. Civil Engineering Department – University of Lahore.
Design of Steel Structures
49
Figure 3.14. Determination of K-value for partially Restrained Columns
The effective length factor of column is determined using
the charts given in the Figure 3.14 expression.
(check Page- 104 on Reference - 1)
Note: The charts does not give the actual values.
50. Civil Engineering Department – University of Lahore.
Design of Steel Structures
K-Values For Truss And Braced Frame Members
The effective length factor, K, is considered equal to 1.0 for
members of the trusses and braced frame columns.
In case the value is to be used less than one for frame
columns, detailed buckling analysis is required to be
carried out and bracing is to be designed accordingly.
50
ELASTIC BUCKLING LOAD FOR LONG
COLUMNS
A column with pin connections on both ends is considered
for the basic derivation, as shown in Figure 3.15.
51. Civil Engineering Department – University of Lahore.
Design of Steel Structures
51
P =
Pcr
P =
Pcr
umax.
u
D
y
C
B
A
Buckled
Shape
L / 2
L / 2
The column has a length equal to L
and is subjected to an axial
compressive load, P.
Buckling of the column occurs at a
critical compressive load, Pcr.
The lateral displacement for the
buckled position at a height y from
the base is u. The bending moment
at this point D is: Figure 3.15. Buckled Elastic
Curve for Long Columns
M = Pcr u (I)
52. Civil Engineering Department – University of Lahore.
Design of Steel Structures
This bending moment is function of the deflection unlike
the double integration method of structural analysis where
it is independent of deflection.
The equation of the elastic curve is given by the Euler-
Bernoulli Equation, which is the same as that for a beam.
EI = M (II)
d u
dy
2
2
or EI + Pcr u = 0
d u
dy
2
2
or + u = 0 (III)
2
2
dy
u
d
EI
Pcr
52
53. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Let = C2 where C is constant (IV)
EI
Pcr
+ C2 u = 0 (V)
2
2
dy
u
d
The solution of this differential equation is:
u = A cos (C y) + B sin (C y) (VI)
where, A and B are the constants of integration.
Boundary Condition No. 1:
At y = 0, u = 0
0 = A cos(0) + B sin (0) A = 0
53
54. Civil Engineering Department – University of Lahore.
Design of Steel Structures
u = B sin (C y) (VII)
Boundary Condition No. 2:
At y = L, u = 0
From Eq. VII: 0 = B sin (C L)
Either B = 0or sin (C L) = 0 (VIII)
If B = 0, the equation becomes u = 0, giving un-deflected
condition. Only the second alternate is left for the
buckled case.
sin (C L) = sin = 0 (IX)
L
EI
Pcr
54
55. Civil Engineering Department – University of Lahore.
Design of Steel Structures
sin = 0 for = 0, , 2, 3, … (radians)
Or n where n = 0, 1, 2, … (X)
Hence, from Eq. IX: = n
L
EI
Pcr
Pcr = (XI)
2
2
2
L
EI
n
The smallest value of Pcr is for n = 1, and is given below:
Pcr = (XII)
2
2
L
EI
55
56. Civil Engineering Department – University of Lahore.
Design of Steel Structures
For other columns with different end conditions, we
have to replace L by the effective length, L e = K L.
Pcr = (XIII)
2
2
KL
EI
Pcr =
2
2
2
KL
Ar
E
Pcr = = Fe A (XIV)
2
2
r
L
K
A
E
and Fe = (XV)
2
2
r
L
K
E
56
57. Civil Engineering Department – University of Lahore.
Design of Steel Structures
It is important to note that the buckling load determined
from Euler equation is independent of strength of the steel
used.
The most important factor on which this load depends is
the KL/r term called the slenderness ratio.
Euler critical buckling load is inversely proportional to
the square of the slenderness ratio.
With increase in slenderness ratio, the buckling strength
of a column drastically reduces.
57
In the above equations:
= slenderness ratio
r
KL
58. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Pcr = Euler’s critical elastic buckling load
Fe = Euler’s elastic critical buckling stress
Long compression members fail by elastic buckling and short
compression members may be loaded until the material yield
or perhaps even goes into the strain-hardening range.
However, in the vast majority of usual situations failure
occurs by buckling after a portion of cross-section has
yielded.
This is known as inelastic buckling. This variation in column
behaviour with change of slenderness ratio is shown in
Figure 3.16.
58
59. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Elastic Buckling
Fy
Fcr
200
C
D
B
A
Rc
Euler’s Curve
(Elastic Buckling)
Compression Yielding
0.44 Fy
Approximately
Short
Columns
Intermediate
Columns
Long Columns
Inelastic Buckling (Straight Line Or
a Parabolic Line Is Assumed)
KL / r (R)
(KL / r)max
20 to 30
59
60. Civil Engineering Department – University of Lahore.
Design of Steel Structures
TYPES OF COLUMNS DEPENDING ON
BUCKLING BEHAVIOUR
Elastic Critical Buckling Stress
The elastic critical buckling stress is defined as under:
Fe = Elastic critical buckling (Euler) stress
= 2
2
r
KL
E
The critical slenderness ratio dividing the expected elastic
and the inelastic buckling is denoted by Rc and is given
below:
60
61. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Rc = 133 for A36 steel
y
F
E
71
.
4
Long Columns
In long columns, elastic buckling is produced and the
deformations are recovered upon removal of the load.
Further, the stresses produced due to elastic buckling
remains below the proportional limit.
The Euler formula is used to find strength of long columns.
Long columns are defined as those columns for which the
slenderness ratio is greater than the critical slenderness
ratio, Rc.
61
62. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Elastic Buckling
c Fy
Maximum
Compressive
Stress (c Fcr)
200
C
Rc
Short
Columns
Intermediate
Columns
Long Columns
Inelastic Buckling
No Buckling
KL / r
(KL / r)max
20 to 30
62
63. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Short Columns
For very short columns, when the slenderness ratio is less
than 20 to 30, the failure stress will equal the yield stress
and no buckling occurs. In practice, very few columns
meet this condition.
For design, these are considered with the intermediate
columns subjected to the condition that failure stress
should not exceed the yield stress.
63
Intermediate Columns
Intermediate columns buckle at a relatively higher load
(more strength) as compared with long columns.
64. Civil Engineering Department – University of Lahore.
Design of Steel Structures
The buckling is inelastic meaning that part of the section
becomes inelastic after bending due to buckling.
The columns having slenderness ratio lesser than the critical
slenderness ratio (Rc) are considered as intermediate
columns, as shown in Figure 3.16.
64
COLUMN STRENGTH FORMULAS
The design compressive strength (cPn) and the allowable
compressive strength (Pn / c) of compression members,
whose elements do not exhibit elastic local instability
(only compact and non-compact sections), are given
below:
65. Civil Engineering Department – University of Lahore.
Design of Steel Structures
c = 0.90 (LRFD) : Pn = Fcr Ag
c = 1.67 (ASD) : Pn = Fcr Ag
Fcr = critical or ultimate compressive strength based on the
limit state of flexural buckling determined as under:
65
Elastic Buckling
When KL / r > Rc or Fe < 0.44Fy
Fcr = 0.877 Fe (AISC Formula E3-2)
where Fe is the Euler’s buckling stress and 0.877 is a
factor to estimate the effect of out-of-straightness of
about 1/1500.
66. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Inelastic Buckling and No Buckling
When KL / r Rc or Fe > 0.44Fy
Fcr = Fy (AISC Formula E3-3)
e
y
F
F
658
.
0
66
TYPES OF COLUMN SECTIONS FOR
LOCAL STABILITY
Compact Sections
A compact section is one that has sufficiently thick
elements so that it is capable of developing a fully plastic
stress distribution before buckling.
The term plastic means stressed throughout to the yield
stress.
67. Civil Engineering Department – University of Lahore.
Design of Steel Structures
For a compression member to be classified as compact, its
flanges must be continuously connected to its web or webs
and the width thickness ratios (b/t) of its compression
elements may not be greater than the limiting ratios p
give in AISC Table B4.1 and reproduced in Table 3.1.
Element p p For A36
Un-stiffened: Defined only for
flexure
Stiffened: Flanges of hollow
sections subjected to
compression.
31.8
y
F
E
12
.
1
67
68. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Non-Compact Sections
A non-compact section is one for which the yield stress
can be reached in some but not all of its compression
elements just at the buckling stage.
It is not capable of reaching a fully plastic stress
distribution.
In AISC Table B4.1, the non-compact sections are
defined as those sections which have width-thickness
ratios (b/t) greater than p but not greater than r.
Values of limiting b/t ratios (r) are given in Table 3.2.
68
69. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Element
Width-
Thickness
Ratio
r
r For A36
Steel
Unstiffened
1. Flanges of I-shaped sections in pure compression,
plates projecting from compression elements,
outstanding legs of pairs of angles in continuous
contact, and flanges of channels in pure
compression.
15.9
2. Legs of single angle struts, legs of double angle
struts with separators and other un-stiffened
elements supported along one edge.
12.8
3. Stems of tees.
21.3
4. Flanges of built-up I-sections with projecting
plates or angles.
t
b
t
b
t
d
t
b
y
F
E
56
.
0
y
F
E
45
.
0
y
F
E
75
.
0
y
c
F
E
k
64
.
0
c
k
1
.
18
69
70. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Element
Width-
Thickness
Ratio r
r For
A36 Steel
Stiffened
1. Flanges of rectangular hollow sections of uniform
thickness used for uniform compression.
39.7
2. Flexure in webs of doubly symmetric I-shaped
sections and channels.
161.8
3. Uniform compression in webs of doubly
symmetric I-shaped sections and uniform
compression in all other stiffened elements.
42.3
4. Circular hollow sections in axial compression.
d / t 0.11 (E / Fy) 88.6
t
b
w
t
h
t
b
y
F
E
40
.
1
y
F
E
70
.
5
y
F
E
49
.
1
70
71. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Slender Compression Sections
These sections consist of elements having width-thickness
ratios greater than r and will buckle elastically before the
yield stress is reached in any part of the section.
A special design procedure for slender compression sections
is provided in Section E7 of the AISC Specification.
However, it will not be covered in detail here.
71
Width Of Un-stiffened Elements
For un-stiffened elements, which are supported along
only one edge parallel to the direction of the
compression force, the width shall be taken as follows:
72. Civil Engineering Department – University of Lahore.
Design of Steel Structures
a. For flanges of I-shaped members and tees, the width
b is half the full nominal width (bf /2).
b. For legs of angles, the width b is the longer leg
dimension.
c. For flanges of channels and zees, the width b is the
full nominal dimension (bf).
d. For plates, the width b is the distance from the free
edge to the first row of fasteners or line of welds.
e. For stems of tees, d is taken as the full nominal
depth.
72
73. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Width Of Stiffened Elements
a. For webs of rolled or formed sections, h is the clear
distance between the flanges less the fillet or
corner radius at each flange and hc is twice the
distance from the centroidal axis to the inside face
of the compression flange less the fillet or corner
radius.
b. For webs of built-up sections,
h is the clear distance between the inner lines of
fasteners on the web or the clear distance between
flanges when welds are used.
73
74. Civil Engineering Department – University of Lahore.
Design of Steel Structures
hc is twice the distance from the centroidal axis to the
nearest line of fasteners at the compression flange or
the inside face of the compression flange when welds
are used, and
hp is twice the distance from the plastic neutral axis to
the nearest line of fasteners at the compression flange
or the inside face of the compression flange when
welds are used.
74
75. Civil Engineering Department – University of Lahore.
Design of Steel Structures
MODIFIED SLENDERNESS RATIO
Snug Tight Connections
Snug tight connection is defined as the type in which the
plates involved in a connection are in firm contact with
each other but without any defined contact prestress.
It usually means the tightness obtained by the full effort
of a man with a wrench or the tightness obtained after a
few impacts of an impact wrench.
Obviously there is some variation in the degree of
tightness obtained under these conditions. The tightness
is much lesser than tensioning of the high-strength bolts.
75
76. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Turn-of-Nut Method: After the tightening of a nut to a snug
fit, the specified pre-tension in high-strength bolts may be
controlled by a predetermined rotation of the wrench.
This procedure is called turn-of-nut method of fixing the
bolts. Slip is allowed in turn-of-nut method.
76
Turn of the nut method (Table 8 –CSA-S16)
1/3 turn for Lb < 4db
1/2 turn for 4db < Lb < 8db (or 200 mm)
2/3 turn for longer bolts
77. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Built-up compression members composed of two or more
hot rolled shapes shall be connected to one another at
intervals by stay plates (shear connectors) such that the
maximum slenderness ratio a / ri of individual element,
between the fasteners, does not exceed the governing
slenderness ratio of the built-up member, that is, the greater
value of (KL / r)x or (KL / r)y for the whole section.
Shear connectors are also required to transfer shear
between elements of a built-up member that is produced
due to buckling of the member.
77
Shear Connections / Stay Plates Between
Elements Of A Built-Up Member
78. Civil Engineering Department – University of Lahore.
Design of Steel Structures
Following notation is used in further discussion of the
effect of spacing of shear connectors:
a = clear distance between connectors
ri = minimum radius of gyration of individual component
a / ri = largest column slenderness of individual component
rib = radius of gyration of individual component relative to
its centroidal axis parallel to member axis of buckling
= column slenderness of built-up member acting as a
unit
= modified column slenderness of the built-up member
as a whole
78
0
r
KL
m
r
KL
79. Civil Engineering Department – University of Lahore.
Design of Steel Structures
= separation ratio = h / (2 rib) , and
h = distance between centroids of individual components
perpendicular to the member axis of buckling
79
Modified Slenderness Ratio Depending
On Spacing Of Stay Plates
If the buckling mode of a built-up compression member
involves relative deformation that produces shear forces in
the connectors between individual parts, the modified
slenderness ratio is calculated as follows:
(a) For snug-tight bolted connectors:
=
m
r
KL
2
2
0
i
r
a
r
KL
80. Civil Engineering Department – University of Lahore.
Design of Steel Structures
(b) for welded connectors and for fully tightened bolted
connectors as required for slip-critical joints:
=
m
r
KL
2
2
2
2
0 1
82
.
0
ib
r
a
r
KL
(KL / r)m should only be used if buckling occurs about
such an axis such that the individual members elongate by
different amounts. (always considered about minor axes)
For example for double angles in Figure 3.17, if buckling
occurs about x-axis, (KL / r)m is not evaluated as both the
angles bend symmetrically without any shear between the
two.
80
81. Civil Engineering Department – University of Lahore.
Design of Steel Structures
However, if buckling occurs about y-axis, one of the
angle sections is elongated while the other is
compressed producing shear between the two and
consequently (KL / r)m is required to be evaluated.
At the ends of built-up compression members bearing
on base plates or milled surfaces, all components in
contact with one another shall be connected by a weld
having a length not less than the maximum width of the
member, or
by bolts spaced longitudinally not more than four
diameters apart for a distance equal to 1.5 times the
maximum width of the member.
81
82. Civil Engineering Department – University of Lahore.
Design of Steel Structures
x
y
The slenderness ratio of individual component between
the connectors (Ka / ri) should not exceed 75% of the
governing slenderness ratio of the built-up member.
Because we do not want local buckling before overall
buckling.
82
83. Civil Engineering Department – University of Lahore.
Design of Steel Structures
83
Fy
Fcr
200
C
D
B
A
KL / r (R)