This document provides information on the design of reinforced concrete columns, including:
- Columns transmit loads vertically to foundations and may resist both compression and bending. Common cross-sections are square, circular and rectangular.
- Columns are classified as braced or unbraced depending on lateral stability, and short or slender based on buckling resistance. Short column design considers axial load capacity while slender column design accounts for second-order effects.
- Reinforcement details include minimum longitudinal bar size and spacing and design of lateral ties. Slender column design determines loadings and calculates moments from stiffness, deflection and biaxial bending effects. Design charts are used to select reinforcement for columns under axial and uniaxial
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
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
Steel structure: Bolted Connection chapter
A bolt is a metal pin with a head formed at one end and shank threaded at the other in order to
receive a nut. On the basis of load transfer in the connection bolts are classified as:
(a) Bearing Type
(b) Friction Grip Type
There are two types of bearing type bolts, namely,
(i) Unfinished or Black Bolts.
(ii) Finished or Turned Bolts.
The shanks of black bolts are unfinished, i.e., rough as obtained at the time of rolling, while
turned bolts are obtained by turning hexagonal shank to circular shape. The bolt hole diameter is
only 1.5 mm larger than that of the shank in case of turned bolt. These bolts are used in special jobs
like connecting machine parts subject to dynamic loadings. For black bolts, diameter of bolt hole is
larger and are used in most of the work. A black bolt is represented as M16, M20, etc. which means
black bolt of nominal diameter 16 mm, black bolt of nominal diameter 20 mm, etc.
-DESIGN STRENGTH OF BEARING BOLTS
-DESIGN STRENGTH OF HSFG BOLTS IN SHEAR (Vdsf)
-PRINCIPLES TO BE OBSERVED IN THE DESIGN
Introduction-Plastic hinge concept-plastic section modulus-shape factor-redistribution of moments-collapse mechanism.
Theorems of plastic analysis - Static/lower bound theorem; Kinematic/upper bound theorem-Plastic analysis of beams and portal frames by equilibrium and mechanism methods.
Steel structure: Bolted Connection chapter
A bolt is a metal pin with a head formed at one end and shank threaded at the other in order to
receive a nut. On the basis of load transfer in the connection bolts are classified as:
(a) Bearing Type
(b) Friction Grip Type
There are two types of bearing type bolts, namely,
(i) Unfinished or Black Bolts.
(ii) Finished or Turned Bolts.
The shanks of black bolts are unfinished, i.e., rough as obtained at the time of rolling, while
turned bolts are obtained by turning hexagonal shank to circular shape. The bolt hole diameter is
only 1.5 mm larger than that of the shank in case of turned bolt. These bolts are used in special jobs
like connecting machine parts subject to dynamic loadings. For black bolts, diameter of bolt hole is
larger and are used in most of the work. A black bolt is represented as M16, M20, etc. which means
black bolt of nominal diameter 16 mm, black bolt of nominal diameter 20 mm, etc.
-DESIGN STRENGTH OF BEARING BOLTS
-DESIGN STRENGTH OF HSFG BOLTS IN SHEAR (Vdsf)
-PRINCIPLES TO BE OBSERVED IN THE DESIGN
Introduction-Plastic hinge concept-plastic section modulus-shape factor-redistribution of moments-collapse mechanism.
Theorems of plastic analysis - Static/lower bound theorem; Kinematic/upper bound theorem-Plastic analysis of beams and portal frames by equilibrium and mechanism methods.
Design of Beam- RCC Singly Reinforced BeamSHAZEBALIKHAN1
Concrete beams are an essential part of civil structures. Learn the design basis, calculations for sizing, tension reinforcement, and shear reinforcement for a concrete beam.
Steel column design plays a crucial role in the construction industry, ensuring the structural integrity and safety of buildings and infrastructure projects. Columns are vertical load-bearing members that support the weight of the structure and transmit it to the foundation. This brief presentation provides an overview of steel column design, highlighting key considerations, design principles, and the importance of adherence to codes and standards.
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Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
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.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
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Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
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.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
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.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
1. Building Project (SPC1)
Design of RC Column
Done by: Eng.S.Kartheepan (M.Sc, B.Eng, AMIESL, AMIIESL)
Department of Civil Engineering
IET, Katunayake
E-mail: karthee2087@gmail.com
2. Introduction to column
• Columns act as vertical supports to beams and
slabs, and to transmit the loads to the
foundations.
• Columns are primarily compression members,
although they may also have to resist bending
moment transmitted by beams.
• Columns may be classified as short or slender,
braced or unbraced depending on various
dimensional and structural factors.
7. Column sections
• Common column cross sections are:
(a) Square
(b) Circular
(c) Rectangular section.
• The greatest dimension should not exceed four
times its smaller dimension. (h≤4b) – Clause 3.8.1
• For h>4b, the member should be regarded as a
wall for design purpose.
8. Failure modes of columns
Compression
failure
Buckling
Column Sections
9. Braced and unbraced column
The basic purpose of column is used to transfer the loads
in a vertical direction to the foundation. Columns can be
categorized into two types based on the lateral restrained.
Such as
1. Braced Column
2. Unbraced Column
Braced Column –
A column may be considered braced in a given plane if
lateral stability to the structure as a whole is provided by
walls or bracing (Clause 3.8.1.5)
Unbraced Column –
It should otherwise be considered as unbraced. It means if
there is no lateral strains then which column is considered
as unbraced column(Clause 3.8.1.5)
15. • A braced column is classified as being short if :
• A column may be considered as short when both
the ratios lex/h and ley/b are less than 15
(braced)
Braced – Short column: Clause 3.8.1.3
16. • A column may be considered as short when both the
ratios lex/h and ley/b are less than 10 (unbraced). It
should otherwise be considered as Slender.
• Short – both lex/h and ley/b < 15 for braced columns
< 10 for unbraced columns
• Braced - If lateral stability to structure as a whole is
provided by walls or bracing designed to resist all lateral
forces in that plane then it is braced column
• Or else – Unbraced
Unbraced – Short column: Clause 3.8.1.3
17. • The effective height, le of a column in a given
plane may be obtained from the following
equation:
Where is a coefficient depending on the fixity at
the column ends and lo is the clear height of the
columns.
• Effective height for a column in two plane
directions may be different.
Effective height of column (Clause - 3.8.1.6,
BS 8110 – Part: 01, 1997)
18. for unbraced column can be obtained from Table 3.20
Effective height of column (Clause - 3.8.1.6,
BS 8110 – Part: 01, 1997)
for braced column can be obtained from Table 3.19
19. End conditions (Clause 3.8.1.6.2, BS1997)
End condition 1 – The end of the column is connected
monolithically to beams on either side which are at least as
deep as the overall dimension of the column in the plane
considered. Where the column is connected to foundation, it
should be designed to carry moment.
20. • End condition 2 – The end of column is connected
monolithically to beams or slabs on either side which are
shallower than the overall dimension of the column in
the plane considered.
End conditions (Clause 3.8.1.6.2, BS1997)
21. • End condition 3 – The end of the column is connected
to members which, while not specifically designed to
provide restraint to rotation of the column will
nevertheless, provide some nominal restraint.
End conditions (Clause 3.8.1.6.2, BS1997)
22. • End condition 4 – The end of the column is
unrestrained against both lateral movement and rotation
(e.g. the free end of a cantilever column in an unbraced
structure)
End conditions (Clause 3.8.1.6.2, BS1997)
24. Data’s: b = 250, h = 350 and Find the effective height.
Answer
25. Reinforcement details: longitudinal reinforcement
(Clause 3.12.5.3, BS 8110)
1. Size and minimum number of bars – bar size should not be
less than 12 mm in diameter. Rectangular column should
reinforced with minimum 4 bars; circular column should
reinforced with minimum 6 bars.
2. The longitudinal reinforcement should not exceed the
following amounts, calculated as percentages of the
gross cross-sectional area of the concrete: (Clause
3.12.6.2)
a) vertically-cast columns: 6 %;
b) horizontally-cast columns: 8 %;
c) laps in vertically- or horizontally-cast columns: 10 %.
3. Spacing of reinforcement – the minimum distance between
adjacent bars should not be less than the diameter of the
bar or hagg + 5 mm.
26. Reinforcement details – links (Clause 3.12.7.1, BS 8110)
• The axial loading on the column may cause buckling
of the longitudinal reinforcement and subsequent
cracking and spalling of concrete cover.
• Links are passing round the bars to prevent buckling.
27. 1. Size and spacing of links – the diameter of the link
should be at least one quarter of the largest
longitudinal bar size or minimum 6 mm. The
maximum spacing is 12 times of the smallest
longitudinal bar.
2. Arrangement of links
Reinforcement details – links (Clause 3.12.7.1, BS 8110)
28. Theoretical strength of reinforced
concrete column
The equation is derived on the assumption that the axial load
is applied perfectly at the centre of the column.
29. Short column design
The short column are divided into three categories:
1. Columns resisting axial load only
B2 Column will resist an axial load only, as it supports
beams equal in length and symmetrically arranged.
30. Clause 3.8.4.3 Nominal eccentricity of short columns
resisting moments and axial force
• To allow for nominal eccentricity, BS 8110 reduce the
theoretical axial load capacity by about 10%.
• Short columns usually need only to be designed for the
maximum design moment about the one critical axis.
Where, due to the nature of the structure, a column
cannot be subjected to significant moments, it may be
designed so that the design ultimate axial load does not
exceed the value of N given by:
• Design maximum axial load capacity of short column is
given in the above.
31. Clause 3.8.4.3 Nominal eccentricity of short columns
resisting moments and axial force
• Normally short columns only require to be designed for
the maximum moment about one critical axis in addition
to the axial load.
• In the case of a column supporting e.g. a rigid structure
or very deep beams, where it cannot be subjected to
significant moments, they may be designed in accordance
with Clause 3.8.4.3
32. Example - Axially loaded column
A short, braced column is subjected to an ultimate applied axial load
of 3000 kN and a nominal moment only. Using the design data given:
1. Check that the column is short
2. Determine the required area of main reinforcement
3. Determine the suitable links
35. 2. Column supporting an approximately
symmetrical arrangement of beams
C2 Column supports a symmetrical arrangement of
beams but which are unequal in length.
If
(a) the loadings on the beam are uniformly
distributed,
(b) the beam spans do not differ by more than 15
percent, the column C2 belongs to category 2.
36. Clause 3.8.4.4 Short braced columns supporting an
approximately symmetrical arrangement of beams
• The column is subjected to axial and small moment
when it supports approximately symmetrical
arrangement of beams:
• The design ultimate axial load for a short column of this
type may be calculated using the following equation:
• The design axial load capacity:
37. Clause 3.8.4.4 Short braced columns supporting an
approximately symmetrical arrangement of beams
• A reduction from the equation given in Clause 3.8.4.3 is
given to allow for moments which will arise from a
symmetrical loading on symmetrical beams and is given
in Clause 3.8.4.4 in the following equation:
38. 3. Columns resisting axial loads and uniaxial or
biaxial bending
If the column does not meet criteria (a) and (b), then
the column belongs to category 3.
A column is considered
biaxially loaded
when the bending occurs
about the X and Y
axes, such as in the case of
the corner column C
39. Column resisting an axial load and uniaxial bending
• For column resisting axial load and bending moment at one
direction, the area of longitudinal reinforcement is
calculated using design charts in Part 3 BS 8110.
• The design charts are available for columns having a
rectangular cross section and symmetrical arrangement of
reinforcement.
• Design charts are derived based on yield stress of 460
N/mm2 for reinforcement steel but the area of
reinforcement obtained will be approximately 10% greater
than required.
• Design charts are available for concrete grades – 25, 30,
35, 40, 45 and 50.
• The d/h ratios are in the range of 0.75 to 0.95 in 0.05
increment.
40. Column resisting an axial load and biaxial bending
• The columns are subjected to an
axial and bending moment in
both x and y directions.
• The columns with biaxial
moments are simplified into the
columns with uniaxial moment
by increasing the moment about
one of the axes then design the
reinforcement according the
increased moment.
41. Column resisting an axial load and biaxial
bending (clause 3.8.4.5, BS 8110)
Symmetrically-reinforced
rectangular sections may be
designed to withstand an
increased moment about one axis
given by the following equations:
43. • Slender or Non-slender column depending on the
sensitivity to second order effect (P- effect)
• Use slenderness ratio, to measure column
vulnerability by elastic instability or buckling
• Non-Slender:
a) Design action are not significantly affected by
deformation (P- effect is small)
b) P- effect can be ignored if does not exceed a
particular value
c) P- effect can be ignored if 10% of the
corresponding first order moments
Classification of Columns
44. • Short column – , crushing at ultimate strength
• Slender column – , buckling under low compressive
load
Compression
failure
Buckling
failure
Classification of Columns
46. Design of slender Column
Load Evaluation in ULS (Ultimate Limit State)
• Load due to roof – design load of roof × Area of roof
• Load due to slab – design load in slab calculation × Area
of slab in the particular column location.
• Load due to Beam – design load in beam calculation ×
total length of beam
• Load due to Column – Column load in each floor level
1. 2nd Floor to Roof level Column
2. 1st Floor to 2nd Floor column
3. Foundation level to Ground Floor Column
Finally total Axial load is estimated in ULS on the column.
47. Design of slender Column
Find the stiffness factor (K)
Stiffness, K = EI/L
Relative Column Stiffness, k =
Kcol/2(Kbeam)
Moment of Inertia, I = bh3/12
BM (Mx)= Relative Column Stiffness × Fixed End BM
48. Design of slender Column
Minimum Eccentricity
All design moment are to be not less than the
design ultimate axial load times the minimum
eccentricity, e(min), equal to 0.05 times the overall
dimension of the column in the plane of bending.
emin = 0.05h
This eccentricity however should not be more than
20 mm.
Where there is biaxial bending, it is only necessary
to consider the nominal eccentricity moment about
one axis at a time.
Mmin = N × emin
49. Design of slender Column
Deflection induced moments in slender columns
The cross sections of the slender columns are
designed as short column but an account is taken
of the additional deflection moments.
The deflection induced additional moment Madd is
given by Eq 35:
The deflection άu for a rectangular column under
ultimate conditions is calculated by the following
(Eq 32):
Here Ba is calculated by using the following Eq 34
50. Design of slender Column
Deflection induced moments in slender columns
In the above, b is generally the smaller dimension of
the column except when considering biaxial bending
and designing in two directions it can be the h
dimension.
K is a reduction factor that corrects the deflection to
allow for the influence of axial load and is calculated
by using Eq 33 as follows:
51. Design of slender Column
Design moments in braced columns bent about a single axis
Figure 3.20 of BS8110 shows the distribution of moments
assumed over the height of a typical braced column.
The initial moment at the point of maximum additional
moment (i.e. near mid-height of the column) is given by Eq
36:
Mi = 0.4M1 + 0.6M2 >= 0.4M2
Where,
M1 is the smaller initial end moment due to design
ultimate loads;
M2 is the larger initial end moment due to design
ultimate loads.
52. Design of slender Column
Design moments in braced columns bent about a single axis
Assuming the column is bent in double curvature, M1
should be taken as negative and M2 positive. As can be seen
from Fig 3.20 of BS 8110, the maximum design moment for
the column will be the greatest of these 4 values:
1) M2;
2) Mi + Madd;
3) M1 + Madd/2;
4) N emin.
53. Biaxial Bending
When designing columns in biaxial bending, symmetrically-
reinforced rectangular sections may be designed to
withstand an increased moment about one axis given by the
following two equations Eq 40 & Eq 41:
a) for Mx/h' >= My/b' Mx' = Mx + B' h'/b' My
b) for Mx/h' < My/b' My' = My + B' b'/h' Mx
where
• h' and b' are shown in Figure 3.22;
• B' is the coefficient obtained
from Table 3.22
54. Design chart for column resisting an axial load and
uniaxial bending moment, (Part 3, BS 8110)