The document summarizes the design of batten plates connecting back-to-back channel sections in a built-up column using both bolt and weld connections. For the bolt connection, 420x340x8mm end batten plates and 420x300x8mm intermediate batten plates are designed to transmit shear and bending forces using four 20mm diameter bolts per connection. For the weld connection, 360x270x6mm end batten plates and 360x220x6mm intermediate batten plates are designed using full penetration welds on all sides to transmit the forces. Both connections are checked to verify the capacities of the bolts/welds are not exceeded.
Niveles de daño a partir de un analisis pushovereliasrojano
Niveles de daño a partir de un analisis pushover para una estructura aporticada en concreto reforzado. tesis de grado universidad industrial de santander.
Niveles de daño a partir de un analisis pushovereliasrojano
Niveles de daño a partir de un analisis pushover para una estructura aporticada en concreto reforzado. tesis de grado universidad industrial de santander.
COLD-FORMED STEEL N1. Diseño de costaneras de sección canal atiesada. AISI S1...AngelManrique7
COLD-FORMED STEEL. BEAM DESIGN
Los elementos de #acero cuya sección transversal se logra mediante el plegado o doblado de planchas de #acero al carbono a temperatura ambiente, se denominan perfiles conformados o laminados en frio. En lo que respecta al desempeño #estructural de estos perfiles, difiere de manera significativa con el comportamiento de los denominados perfiles laminados o rodados en caliente. Esto, sobre todo por la susceptibilidad al denominado pandeo distorsional y torsional, influido por el uso predominante de elementos con espesores muy pequeños en función a su tamaño, es decir, la presencia de elementos esbeltos.
Para el diseño de los perfiles conformados en frio, el Instituto Americano del Hierro y Acero (#AISI) ha publicado diferentes especificaciones que contempla como abarcar de manera eficaz y precisa todos los requerimientos mínimos para garantizar el correcto funcionamiento #estructural de estos elementos.
Because of torsion, the beam fails in diagonal tension forming the spiral cracks around the beam. Warping of the section does not allow a plane section to remain as plane after twisting. Clause 41 of IS 456:2000 provides the provisions for
the design of torsional reinforcements. The design rules for torsion are based on the equivalent moment.
ANALYSIS & DESIGN ASPECTS OF PRE-STRESSED MEMBERS USING F.R.P. TENDONSGirish Singh
The purpose of this investigation is mainly a brief explanation about the advantages of FRP over steel. The various uses and advantages of FRP are explained in this project. In this project, we have taken a section of 3m length, 200mm width and 300mm depth and using a parabolic tendon of eccentricity 100mm at the centre. We have design the section for FRP as well as steel with the above data. The final stresses obtained is being verified with the help of Ansys software. We have shown the result of steel straight tendon only in this mini project.
Solution Manual for Structural Analysis 6th SI by Aslam Kassimaliphysicsbook
https://www.unihelp.xyz/solution-manual-structural-analysis-kassimali/
Solution Manual for Structural Analysis - 6th Edition SI Edition
Author(s): Aslam Kassimali
Solution Manual for 6th SI Edition (above Image) is provided officially. It include all chapters of textbook (chapters 2 to 17) plus appendixes B, C, D.
Lec.2 statically determinate structures & statically indeterminate struct...Muthanna Abbu
The student will learn the determination of internal forces in different structures and the
kind of forces distribution due to external & internal effects .He will also learn about the
structures deformation due to these effects .
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Gantry girder
Gantry girder or crane girder hand operated or electrically operated overhead cranes in industrial building such as factories, workshops, steel works, etc. to lift heavy materials, equipment etc. and carry them from one location to other , within the building
The GANTRY GIRDER spans between brackets attached to columns, which may either be of steel or reinforced concrete. Thus the span of gantry girder is equal to centre to centre spacing of columns. The rails are mounted on gantry girders.
Loads acting on gantry girder
Gantry girder, having no lateral support in its length (laterally unsupported) has to withstand the following loads:
1. Vertical loads from crane :
Self weight of crane girder
Hook load
Weight of crab (trolley)
2. Impact load from crane :
As the load is lifted using the crane hook and moved from one place to another, and released at the required place, an impact is felt on the gantry girder.
3. Longitudinal horizontal force (Drag force) :
This is caused due to the starting and stopping of the crane girder moving over the crane rails, as the crane girder moves longitudinally, i.e. in the direction of gantry girder.
This force is also known as braking force, or drag force.
This force is taken equal to 5% of the static wheel loads for EOT or hand operated cranes.
4. Lateral load (Surge load) :
Lateral forces are caused due to sudden starting or stopping of the crab when moving over the crane girder.
Lateral forces are also caused when the crane is dragging weights across the' floor of the shop.
Types of gantry girders
Depending upon the span and crane capacity, there can be many forms of gantry girders. Some commonly used forms are shows in fig .
Rolled steel beams with or without plates, channels or angles are normally used for spans up to 8m and for cranes up to 50kN capacity.
Plate girder are suitable up to span 6 to 10 m.
Plate girder with channels, angles, etc. can be used for spans more than 10m
Box girder are used foe spans more than 12m.
COLD-FORMED STEEL N1. Diseño de costaneras de sección canal atiesada. AISI S1...AngelManrique7
COLD-FORMED STEEL. BEAM DESIGN
Los elementos de #acero cuya sección transversal se logra mediante el plegado o doblado de planchas de #acero al carbono a temperatura ambiente, se denominan perfiles conformados o laminados en frio. En lo que respecta al desempeño #estructural de estos perfiles, difiere de manera significativa con el comportamiento de los denominados perfiles laminados o rodados en caliente. Esto, sobre todo por la susceptibilidad al denominado pandeo distorsional y torsional, influido por el uso predominante de elementos con espesores muy pequeños en función a su tamaño, es decir, la presencia de elementos esbeltos.
Para el diseño de los perfiles conformados en frio, el Instituto Americano del Hierro y Acero (#AISI) ha publicado diferentes especificaciones que contempla como abarcar de manera eficaz y precisa todos los requerimientos mínimos para garantizar el correcto funcionamiento #estructural de estos elementos.
Because of torsion, the beam fails in diagonal tension forming the spiral cracks around the beam. Warping of the section does not allow a plane section to remain as plane after twisting. Clause 41 of IS 456:2000 provides the provisions for
the design of torsional reinforcements. The design rules for torsion are based on the equivalent moment.
ANALYSIS & DESIGN ASPECTS OF PRE-STRESSED MEMBERS USING F.R.P. TENDONSGirish Singh
The purpose of this investigation is mainly a brief explanation about the advantages of FRP over steel. The various uses and advantages of FRP are explained in this project. In this project, we have taken a section of 3m length, 200mm width and 300mm depth and using a parabolic tendon of eccentricity 100mm at the centre. We have design the section for FRP as well as steel with the above data. The final stresses obtained is being verified with the help of Ansys software. We have shown the result of steel straight tendon only in this mini project.
Solution Manual for Structural Analysis 6th SI by Aslam Kassimaliphysicsbook
https://www.unihelp.xyz/solution-manual-structural-analysis-kassimali/
Solution Manual for Structural Analysis - 6th Edition SI Edition
Author(s): Aslam Kassimali
Solution Manual for 6th SI Edition (above Image) is provided officially. It include all chapters of textbook (chapters 2 to 17) plus appendixes B, C, D.
Lec.2 statically determinate structures & statically indeterminate struct...Muthanna Abbu
The student will learn the determination of internal forces in different structures and the
kind of forces distribution due to external & internal effects .He will also learn about the
structures deformation due to these effects .
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Gantry girder
Gantry girder or crane girder hand operated or electrically operated overhead cranes in industrial building such as factories, workshops, steel works, etc. to lift heavy materials, equipment etc. and carry them from one location to other , within the building
The GANTRY GIRDER spans between brackets attached to columns, which may either be of steel or reinforced concrete. Thus the span of gantry girder is equal to centre to centre spacing of columns. The rails are mounted on gantry girders.
Loads acting on gantry girder
Gantry girder, having no lateral support in its length (laterally unsupported) has to withstand the following loads:
1. Vertical loads from crane :
Self weight of crane girder
Hook load
Weight of crab (trolley)
2. Impact load from crane :
As the load is lifted using the crane hook and moved from one place to another, and released at the required place, an impact is felt on the gantry girder.
3. Longitudinal horizontal force (Drag force) :
This is caused due to the starting and stopping of the crane girder moving over the crane rails, as the crane girder moves longitudinally, i.e. in the direction of gantry girder.
This force is also known as braking force, or drag force.
This force is taken equal to 5% of the static wheel loads for EOT or hand operated cranes.
4. Lateral load (Surge load) :
Lateral forces are caused due to sudden starting or stopping of the crab when moving over the crane girder.
Lateral forces are also caused when the crane is dragging weights across the' floor of the shop.
Types of gantry girders
Depending upon the span and crane capacity, there can be many forms of gantry girders. Some commonly used forms are shows in fig .
Rolled steel beams with or without plates, channels or angles are normally used for spans up to 8m and for cranes up to 50kN capacity.
Plate girder are suitable up to span 6 to 10 m.
Plate girder with channels, angles, etc. can be used for spans more than 10m
Box girder are used foe spans more than 12m.
Content;
1. Top spherical dome.
2. Top ring beam.
3. Cylindrical wall.
4. Bottom ring beam.
5. Conical dome.
6. Circular ring beam.
The basics of enticing water tank design and the related components are broadly calculated in this document. The next few documents will demonstrate the design of Intze tank members like column, bracing and foundation. Keep following the updates.....
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
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.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
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.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
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.
2. Example: A batten column of 10-m long is carrying a factored
load of 1150 kN. The column is restrained in position but not in
direction at both ends. Design a built up column using channel
sections placed back to back.
Design batten plates using bolt connection.
3. Let us try two ISMC 350 @ 413 N/m
Relevant properties of ISMC 350 [ Table II SP 6 (1): 1964]
𝐴 = 5366 mm2, 𝑟𝑧𝑧 = 136.6 mm,
𝑟𝑦𝑦 = 28.3 mm 𝑡𝑓 = 13.5 mm
𝐼𝑧𝑧 = 10008 × 104 mm4 𝐼𝑦𝑦 = 430.6 × 104 mm4
𝑐𝑦𝑦 = 24.4 mm 𝑏 = 100 mm
Solution:
Design of column:
𝑃 = 1150 kN = 1150 × 103 N
L = 1.0 × 10 × 103 = 10000 mm
Let design axial compressive stress for the column be 125 MPa
Required area =
1150×103
125
= 9200 mm2
4. For
𝐾𝐿
𝑟 𝑒
= 80.53, 𝑓𝑦 = 250 MPa and buckling class c, the
design compressive stress from Table 9c of IS 800 :2007
𝑓𝑐𝑑 = 136 −
136−121
10
× 0.53 = 135.2 MPa
Therefore load carrying capacity = 𝐴𝑒𝑓𝑐𝑑
= 10732 × 135.2 × 10−3
= 1451 kN > 1200 kN, OK
Area provided = 2 × 5366 = 10732 mm2
𝐿
𝑟𝑧𝑧
=
10000
136.6
= 73.21
The effective slenderness ratio,
𝐾𝐿
𝑟 𝑒
= 1.1 × 73.21
= 80.53 < 180; ok
5. Spacing of channels:
2𝐼𝑧𝑧 = 2 𝐼𝑦𝑦 + 𝐴
𝑆
2
+ 𝐶𝑦𝑦
2
or 2 × 10008 × 104 = 2 × 430.6 × 104 + 5366
𝑆
2
+ 24.4
2
⇒ 𝑆 = 218.4 mm
Let us keep the channels at a spacing of 220 mm
Spacing of battens:
As per clause 7.7.3 of IS 800: 2007,
𝐶
𝑟𝑦𝑦
< 0.7𝜆
𝑜𝑟 𝐶 < 0.7 × 𝜆 × 𝑟𝑦𝑦 = 0.7 × 80.53 × 28.3 = 1595.3 mm
Also
𝐶
𝑟𝑦𝑦
< 50 or 𝐶 < 50 × 28.3 = 1415 mm
Hence, provide battens at a spacing of 1400 mm.
6. Size of end battens (cl. 7.7.2.3 of IS 800 :2007):
Provide 20 mm bolts.
Edge distance = 1.5 × ℎ𝑜𝑙𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 [Cl. 10.2.4.2 IS 800:2007]
= 1.5 × 20 + 2 = 33 mm
Effective depth = 𝑠 + 𝐶𝑦𝑦
= 220 + 2 × 24.4 = 268.8 mm > 2 × 100 mm
Hence, chosen effective depth is safe.
Overall depth = 268.8 + 2 × 33 = 334.8 mm
Required thickness of batten =
1
50
× 220 + 2 × 50 = 6.4 mm
Length of batten = 220 + 2 × 100 = 420 mm
Provide 420×340×8 mm end batten plates.
7. Size of intermediate battens (cl. 7.7.2.3 of IS 800 :2007):
Effective depth =
3
4
× (220 + 2 × 𝐶𝑦𝑦)
=
3
4
× (220 + 2 × 24.4) = 201.6 mm
> 2 × 100 = 200 mm
Hence adopt an effective depth of 210 mm
Overall depth = 210 + 2 × 33 = 276 mm
Therefore, provide a 420×300×8 mm batten plates @1400 mm
c/c.
8. Design forces:
Transverse shear, 𝑉 =
2.5
100
× 𝑃 =
2.5
100
× 1150 × 103
= 28750 N
Longitudinal shear 𝑉𝑙 =
𝑉𝐶
𝑁𝑆
Spacing of battens, C = 1400 mm
N = No of parallel planes of battens = 2
S = minimum transverse distance between the centroid of the
bolt/weld group = 220 + 2 × 50 = 320 mm
∴ 𝑉𝑙 =
28750×1400
2×320
= 62891 N
Moment, 𝑀 =
𝑉𝐶
2𝑁
=
28750×1400
2×2
= 10.06 × 106 N-mm
10. Connection:
The connection should be designed to transmit both shear and
bending moment.
Assuming 20 mm diameter bolts.
Strength of bolt in single shear
=
𝐴𝑛𝑏×𝑓𝑢𝑏
3×𝛾𝑚𝑏
=
0.78×
𝜋×202
4
×400
3×1.25
× 10−3= 45.27 kN
Minimum pitch, p = 2.5d=2.5×20=50 mm
Minimum end distance, e = 1.5 d0 =1.5×22=33 mm
Provide p = 60 mm and e = 35 mm
kb is smaller of 35/(3×22), 60/(3×22)-0.25, 400/410, 1
Kb = 0.53
11. Strength of bolt in bearing = 2.5𝑘𝑏𝑑𝑡𝑓𝑢/𝛾𝑚𝑏
= 2.5 × 0.53 × 20 × 8 ×
410
1.25
× 10−3 = 69.5 kN
Hence, strength of bolt = 45.27 kN
Number of bolts required =
62891
45.27×103 = 1.39
Let us provide four bolts to take account the stresses due to
bending moments as well.
Check for combined action: For end battens
Force in each bolt due to shear =
62891
4
= 15723 N
Pitch provided = (D-2e)/3= (340-2×35)/3 = 90 mm.
𝑟2 = 2[(90/2)2+(90+90/2)2) = 2[452+1352] = 40500 mm2
12. Force due to moment =
𝑀𝑟
𝑟2 =
10.06×106×135
40500
= 33533 N
Resultant force = 157232 + 335332
= 37036 N = 37 kN < 45.26 kN
Hence safe.
Check for combined action: For intermediate battens
Force in each bolt due to shear =
62891
4
= 15723 N
Pitch provided = (D-2e)/3= (300-2×35)/3 = 77 mm.
𝑟2 = 2[(77/2)2+(77+77/2)2) = 2[38.52+115.52] = 29645 mm2
Force due to moment =
𝑀𝑟
𝑟2 =
10.06×106×115.5
29645
= 39195 N
Resultant force = 157232 + 391952
= 42231N = 42.23 kN < 45.26 kN
Hence safe.
13. ISMC 350
350 mm
220 mm
220 mm
1400
mm
Intermediate batten
420 mm×300 mm×8 mm
End batten
420 mm×340 mm×8 mm
20 mm bolt
Channels back-to-back connected by bolts:
15. Example: A batten column of 10-m long is carrying a factored
load of 1150 kN. The column is restrained in position but not in
direction at both ends. Design a built up column using channel
sections placed back to back.
Design batten plates using weld connection.
16. Let us try two ISMC 350 @ 413 N/m
Relevant properties of ISMC 350 [ Table II SP 6 (1): 1964]
𝐴 = 5366 mm2, 𝑟𝑧𝑧 = 136.6 mm,
𝑟𝑦𝑦 = 28.3 mm 𝑡𝑓 = 13.5 mm
𝐼𝑧𝑧 = 10008 × 104 mm4 𝐼𝑦𝑦 = 430.6 × 104 mm4
𝑐𝑦𝑦 = 24.4 mm 𝑏 = 100 mm
Solution:
Design of column:
𝑃 = 1150 kN = 1150 × 103 N
L = 1.0 × 10 × 103 = 10000 mm
Let design axial compressive stress for the column be 125 MPa
Required area =
1150×103
125
= 9200 mm2
17. For
𝐾𝐿
𝑟 𝑒
= 80.53, 𝑓𝑦 = 250 MPa and buckling class c, the
design compressive stress from Table 9c of IS 800 :2007
𝑓𝑐𝑑 = 136 −
136;121
10
× 0.53 = 135.2 MPa
Therefore load carrying capacity = 𝐴𝑒𝑓𝑐𝑑
= 10732 × 135.2 × 10;3
= 1451 kN > 1200 kN, OK
Area provided = 2 × 5366 = 10732 mm2
𝐿
𝑟𝑧𝑧
=
10000
136.6
= 73.21
The effective slenderness ratio,
𝐾𝐿
𝑟 𝑒
= 1.1 × 73.21
= 80.53 < 180; ok
18. Spacing of channels:
2𝐼𝑧𝑧 = 2 𝐼𝑦𝑦 + 𝐴
𝑆
2
+ 𝐶𝑦𝑦
2
or 2 × 10008 × 104 = 2 × 430.6 × 104 + 5366
𝑆
2
+ 24.4
2
⇒ 𝑆 = 218.4 mm
Let us keep the channels at a spacing of 220 mm
Spacing of battens:
As per clause 7.7.3 of IS 800: 2007,
𝐶
𝑟𝑦𝑦
< 0.7𝜆
𝑜𝑟 𝐶 < 0.7 × 𝜆 × 𝑟𝑦𝑦 = 0.7 × 80.53 × 28.3 = 1595.3 mm
Also
𝐶
𝑟𝑦𝑦
< 50 or 𝐶 < 50 × 28.3 = 1415 mm
Hence, provide battens at a spacing of 1400 mm.
19. Size of end battens (cl. 7.7.2.3 of IS 800 :2007):
Overall depth of batten = 220 + 2 × 𝐶𝑦𝑦
= 220 + 2 × 24.4 = 268.8 ≈ 270 mm
Required thickness of batten =
1
50
× 220 = 4.4 mm
Adopt battens with the thickness of 6-mm
Let provide a 70 mm overlap of battens on channel flange for
welding.
[Overlap > 4 t = 4 × 6 = 24 mm] OK
Length of batten = 220 + 2 × 70 = 360 mm
Provide 360×270×6 mm end batten plates.
20. Size of intermediate battens (cl. 7.7.2.3 of IS 800 :2007):
Overall depth =
3
4
× (220 + 2 × 𝐶𝑦𝑦)
=
3
4
× (220 + 2 × 24.4) = 201.6 mm
> 2 × 100 = 200 mm
Hence adopt overall depth of 220 mm
Therefore, provide a 360×220×6 mm batten plates.
21. Design forces:
Transverse shear, 𝑉 =
2.5
100
× 𝑃 =
2.5
100
× 1150 × 103
= 28750 N
Longitudinal shear 𝑉𝑙 =
𝑉𝐶
𝑁𝑆
Spacing of battens, C = 1400 mm
N = No of parallel planes of battens = 2
S = minimum transverse distance between the centroid of the
bolt/weld group = 220 + 2 × 50 = 320 mm
∴ 𝑉𝑙 =
28750×1400
2×320
= 62891 N
Moment, 𝑀 =
𝑉𝐶
2𝑁
=
28750×1400
2×2
= 10.06 × 106 N-mm
23. Design of weld:
Welding is done on all the four sides as shown in the figure.
Let 𝑡 = throat thickness of weld.
𝐼𝑧𝑧 = 2 ×
70 × 𝑡3
12
+ 70 × 𝑡 ×
220
2
2
+
2 × 𝑡 × 2203
12
Neglecting the term 2 ×
70×𝑡3
12
being insignificant.
Therefore, 𝐼𝑧𝑧 = 346.87 × 104𝑡 mm4
𝐼𝑦𝑦 = 2 ×
𝑡 × 703
12
+ 2 ×
220 × 𝑡3
12
+ 2 × 220 × 𝑡 ×
70
2
2
Neglecting the term 2 ×
220×𝑡3
12
being insignificant.
Therefore, 𝐼𝑦𝑦 = 59.62 × 104𝑡 mm4
24. 𝐼𝑝 = 𝐼𝑧𝑧 + 𝐼𝑦𝑦 = 346.87 × 104
𝑡 + 59.62 × 104
𝑡
= 406.49 × 104
𝑡 mm4
𝑟 =
220
2
2
+
70
2
2
= 115.43 mm
𝑐𝑜𝑠𝜃 =
35
115.43
= 0.30
Direct shear stress (cl. 10.5.9 of IS 800:2007)
=
62891
2×70:2×220 𝑡
=
108.43
𝑡
N/mm2
Shear stress due to bending moment =
10.06×106×115.43
406.49×104𝑡
=
285.67
𝑡
N/mm2
25. Combined stress due to shear and bending
=
108.43
𝑡
2
+
285.67
𝑡
2
+ 2 ×
108.43
𝑡
×
285.67
𝑡
× 0.3
=
334.59
𝑡
<
410
3 × 1.25
= 189.4
or 𝑡 = 1.77 mm
Size of weld = 1.77/0.7 = 2.5 mm
The size of weld should not be less than 5 mm for 13.5 mm
flange.
Hence provide a 5 mm weld to make the connection.
26. ISMC 350
350 mm
220 mm
220 mm
1400
mm
Intermediate batten
360 mm×220 mm×6 mm
End batten
360 mm×270 mm×6 mm
5 mm weld
Channels back-to-back connected by welding:
28. Splices
• A joint when provided in the length of a member is called
splices.
• If a compression member is loaded concentrically,
theoretically no splice is required.
• However, the load is never truly axial and the real column has
to resist bending due to this eccentrically applied load.
Column sections can be spliced in the following cases:
1. When the length of the column is more than the length of
the column section available.
2. In case of multistorey buildings, the section of the column
required for the various storey may be different, as the
load goes on increasing for columns of the lower storeys.
29. Specifications for the design of splices
• Where the ends of the compression members are faced
for complete bearing over the whole area, these should be
spliced to hold the connected members accurately in
position, and to resist any tension when bending is
present.
• Where such members are not faced for complete bearing,
splices should be design to transmit all the forces to
which these are subjected.
• Splices are designed as short columns.
31. Steps for the design of splice
1. For axial compressive load the splice plates are provided
on the flanges of the two column sections to be spliced.
If the column has machined ends, the splice is designed only
to keep the columns in position and to carry tension due to the
bending moment to which it may be subjected. The splice
plate and the connection should be design to carry 50% of the
axial load and tension.
If the ends are not machined, the splice and connections are
design to resist the total axial load and any tension, if present
due to the bending moment.
32. Steps for the design of splice
• The load for the design of splice and connection due to axial
load,
𝑃𝑢1 =
𝑃𝑢
4
(for machined ends)
𝑃𝑢1 =
𝑃𝑢
2
(for non machined ends)
Where, 𝑃𝑢 is the axial factored load.
• The load for the design of splice and connection due
bending moment,
𝑃𝑢2 =
𝑀𝑢
𝑙𝑒𝑣𝑒𝑟 𝑎𝑟𝑚
Where, lever arm is the c/c distance of the two splice plates and
𝑀𝑢 is the factored bending moment.
33. Steps for the design of splice
2. Splice plates are assumed to act as short columns (with zero
slenderness ratio). So these plates will be subjected to yield
stress (𝑓𝑦).
3. The cross-sectional area of the splice plate is calculated by
dividing the appropriate portion of the factored load coming
over the splice by the yield stress.
c/s area required =
𝑃𝑢1+𝑃𝑢2
𝑓𝑦
4. The width of splice plate is usually kept equal to the width of
the column flange.
Width of splice = 𝑏𝑓 (width of flange)
The thickness of the splice plate can be found by dividing the
c/s area of the plates with its width.
34. Steps for the design of splice
5. Nominal diameter of bolts for connection is assumed and the
strength of the bolt is computed.
6. In case of bearing plate is to be designed between two
column sections, the length and width of the plate are kept
equal to the size of lower-storey column and the thickness is
computed by equating the ultimate moment due to the factored
load to the moment of resistance of plate section.
35. Example: A column ISHB 300 @ 576.8 N/m is to support a
factored axial load of 500 kN, shear force of 120 kN and
bending moment of 40 kNm. Design the splice plate and
connection using 4.6 grade bolts. Use steel of grade Fe 410.
Solution:
For steel of grade Fe 410: 𝑓𝑢 = 410 MPa, 𝑓𝑦 = 250 Mpa
For bolts of grade 4.6: 𝑓𝑢𝑏 = 400 MPa
Partial safety factors for material:(Table 5 IS 800:2007)
𝛾𝑚0 = 1.10 𝛾𝑚𝑏 = 1.25
The relevant properties of ISHB 300 @ 576.8 N/m are (Table I,
SP 6-1)
𝐴 = 7485 mm2 𝑏𝑓 = 250 mm,
𝑡𝑓 = 10.6 mm 𝑡𝑤 = 7.6 mm
36. Assume the ends of the column sections to be machined for
complete bearing. As the column ends are flush, it is assumed that
50% of the load is transferred directly and 50% is transferred
through the splice and fastenings. Therefore,
The direct load on each splice plate = 50% 𝑜𝑓
500
2
= 125 kN
Load on splice due to moment =
𝑀𝑢
𝑙𝑒𝑣𝑒𝑟 𝑎𝑟𝑚
=
40×103
300+6
= 130.72 kN
(Assuming 6 mm thick splice plate, the lever arm = 300 + 6 mm)
Total design load for splice, 𝑃𝑠 = 125 + 130.72 = 255.72 kN
Sectional area of splice plate required =
𝑃𝑠
𝑓𝑦
=
255.72×103
250
= 1022.9 mm2
37. Width of the splice plate should be kept equal to the width of
the flange.
Here, the width of the splice plate = 250 mm
Hence, thickness of splice plate =
1022.9
250
= 4.09 mm ≮ 6 mm
Provide a 250×6 mm splice plate.
The length of the splice plate depends upon the number of
bolts in vertical row.
Let us provide 20 mm diameter bolts of grade 4.6.
Strength of 20 mm diameter bolt in single shear (cl. 10.3.3, IS
800:2007)
=
𝐴𝑛𝑏
𝑓𝑢𝑏
3
𝛾𝑚𝑏
=
245×
400
3
1.25
× 10−3 = 45.26 kN
38. Strength of bolt in bearing = 2.5𝑘𝑏𝑑𝑡𝑓𝑢/𝛾𝑚𝑏 (cl. 10.3.4, IS
800:2007)
For 20 mm diameter bolts the minimum edge distance,
𝑒 = 1.5 × 𝑑0 = 1.5 × 20 + 2 = 33 mm
The minimum pitch, p = 2.5 × 20 = 50 mm
Let us provide an edge distance (e) of 35 mm and pitch (p) of
60 mm.
𝑘𝑏 is smaller of
𝑒
3𝑑0
=
35
3×22
= 0.53 ,
𝑝
3𝑑0
− 0.25 =
60
3×22
− 0.25 = 0.66 ,
𝑓𝑢𝑏
𝑓𝑢
=
400
410
= 0.98 and 1.0
Hence 𝑘𝑏 = 0.53
39. ∴ Strength in bearing = 2.5 × 0.53 × 20 × 6 ×
410
1.25
× 10−3
= 52.15 kN
Hence, the strength of bolt (Bv) = 45.26 kN
Number of bolts required, n =
𝑃𝑠
𝐵𝑣
=
255.72
45.26
= 5.65 ≈ 6
Provide 6 bolts for each splice.
Length of the splice plate = 2 × (2 × 60 + 2 × 35) = 380 mm
Provide a splice plate 380×250×6 mm on column flanges as
shown in the figure.
41. Example: A column ISHB 300 @ 576.8 N/m is to support a
factored axial load of 500 kN, shear force of 120 kN and
bending moment of 40 kNm. Design the splice plate and
connection using 4.6 grade bolts. Use steel of grade Fe 410.
42. Solution:
For steel of grade Fe 410: 𝑓𝑢 = 410 MPa, 𝑓𝑦 = 250 Mpa
For bolts of grade 4.6: 𝑓𝑢𝑏 = 400MPa
Partial safety factors for material:(Table 5 IS 800:2007)
𝛾𝑚0 = 1.10𝛾𝑚𝑏 = 1.25
The relevant properties of ISHB 300 @ 576.8 N/m are (Table I,
SP 6-1)
𝐴 = 7485 mm2𝑏𝑓 = 250 mm,
𝑡𝑓 = 10.6mm 𝑡𝑤 = 7.6 mm
43. Assume the ends of the column sections to be machined for
complete bearing. As the column ends are flush, it is assumed that
50% of the load is transferred directly and 50% is transferred
through the splice and fastenings. Therefore,
The direct load on each splice plate = 50% 𝑜𝑓
500
2
= 125 kN
Load on splice due to moment =
𝑀𝑢
𝑙𝑒𝑣𝑒𝑟 𝑎𝑟𝑚
=
40×103
300+6
= 130.72 kN
(Assuming 6 mm thick splice plate, the lever arm = 300 + 6 mm)
Total design load for splice, 𝑃𝑠 = 125 + 130.72 = 255.72 kN
Sectional area of splice plate required =
𝑃𝑠
𝑓𝑦
=
255.72×103
250
= 1022.9mm2
44. Width of the splice plate should be kept equal to the width of
the flange.
Here, the width of the splice plate = 250 mm
Hence, thickness of splice plate =
1022.9
250
= 4.09 mm ≮ 6 mm
Provide a 250×6 mm splice plate.
The length of the splice plate depends upon the number of
bolts in vertical row.
Let us provide 20 mm diameter bolts of grade 4.6.
Strength of 20 mm diameter bolt in single shear (cl. 10.3.3, IS
800:2007)
=
𝐴𝑛𝑏
𝑓𝑢𝑏
3
𝛾𝑚𝑏
=
245 ×
400
3
1.25
× 10−3
= 45.26 kN
45. Strength of bolt in bearing = 2.5𝑘𝑏𝑑𝑡𝑓𝑢/𝛾𝑚𝑏(cl. 10.3.4, IS
800:2007)
For 20 mm diameter bolts the minimum edge distance,
𝑒 = 1.5 × 𝑑0 = 1.5 × 20 + 2 = 33 mm
The minimum pitch, p = 2.5 × 20 = 50 mm
Let us provide an edge distance (e) of 35 mm and pitch (p) of
60 mm.
𝑘𝑏 is smaller of
𝑒
3𝑑0
=
35
3×22
= 0.53 ,
𝑝
3𝑑0
− 0.25 =
60
3×22
− 0.25 = 0.66 ,
𝑓𝑢𝑏
𝑓𝑢
=
400
410
= 0.98 and 1.0
Hence 𝑘𝑏 = 0.53
46. ∴ Strength in bearing = 2.5 × 0.53 × 20 × 6 ×
410
1.25
× 10−3
= 52.15kN
Hence, the strength of bolt (Bv) = 45.26 kN
Number of bolts required, n =
𝑃𝑠
𝐵𝑣
=
255.72
45.26
= 5.65 ≈ 6
Provide 6 bolts for each splice.
Length of the splice plate = 2 × (2 × 60 + 2 × 35) = 380 mm
Provide a splice plate 380×250×6 mm on column flanges as
shown in the figure.
47. Splice plates for shear:
The splice plate for the shear force is provided on the web. A pair
of splice plate (one on each side of web) are provided.
Let us provide 20 mm diameter bolts of grade 4.6.
Strength of bolt in double shear = 45.26 × 2 = 90.52 kN
Strength in bearing = 2.5𝑘𝑏𝑑𝑡𝑓𝑢/𝛾𝑚𝑏
Where, 𝑘𝑏 = 0.53 (taking 𝑒 = 35 mm and p = 60 mm),
𝑡 = 7.6 mm (web thickness)
∴ Strength in bearing = 2.5 × 0.53 × 20 × 7.6 ×
410
1.25
× 10−3 =
66.06 kN
Hence, strength of 20 mm bolt = 66.06kN
48. Shear force in the web, 𝑉 = 120 kN
Number of bolts required =
120
66.06
= 1.8 ≈ 2
Provide 2, 20 mm diameter bolts on each side of the splice.
Length of the splice plate = 4 × 35 = 140 mm
Width of the splice plate = 60 + 2 × 35 = 130 mm
Design shear strength of splice plate (cl. 8.4, IS 800:2007),
𝑉𝑑 =
𝑓𝑦
3 × 𝛾𝑚0
× ℎ × 𝑡
=
250
3 × 1.1
× 130 × 2𝑡𝑠 × 10−3
= 34.12 𝑡𝑠 kN
49. Now, 𝑉𝑑 > 𝑉
or 34.12 𝑡𝑠 > 120
Thickness of the splice plate required,
𝑡𝑠 =
120
34.12
= 3.52 mm ≮ 6mm
So provide a pair of 140×130×6 mm shear splice plates on each
side of the web as shown in the figure.
52. INTRODUCTION
• Flexural members or bending members are commonly called
BEAMS.
• A beam is a structural member subjected to transverse loads
i.e., loads perpendicular to the longitudinal axis.
• The load produce Bending moment & Shear forces.
54. DIFFERENT TYPES OF BEAMS
• JOIST: A closely spaced beams supporting floors or roofs of
building but not supporting the other beams.
• GIRDER: A large beam, used for supporting a number of
joists.
• PURLIN: Purlins are used to carry roof loads in trusses.
• STRINGER: In building, beams supporting stair steps; in
bridges a longitudinal beam supporting deck floor & supported
by floor beam.
• FLOOR BEAM: A major beam supporting other beams in a
building; also the transverse beam in bridge floors.
55. • SPANDREL BEAM: In a building, a beam on the outside
perimeter of a floor, supporting the exterior walls and outside
edge of the floor
• GIRT: A horizontal beam spanning the wall columns of
industrial buildings used to support wall coverings is called a
GIRT.
• RAFTER: A roof beam usually supported by purlins.
• LINTELS: This type of beams are used to support the loads
from the masonry over the openings .
DIFFERENT TYPES OF BEAMS
56. NATURE OF FORCES ACTING ON BEAMS
• It is assumed that the beam is subjected to only transverse
loading.
• All the loads and sections lie in the plane of symmetry.
• It follows that such a beam will be primarily subjected to
bending accompanied by shear in the loading plane with no
external torsion and axial force.
57. • The problem of torsion can not completely be avoided in a
beam even if the beam shape is symmetrical and loads are in
the plane of symmetry.
• The reason is the instability caused by compressive stresses.
Such instability is defined as LATERAL BUCKLING .
When it is involving only local components of a beam it is
called LOCAL BUCKLING.
• Local buckling is a function of width-thickness ratio.
NATURE OF FORCES ACTING ON BEAMS
58. Primary modes of failure of beams are as follows:
1. Bending failure
2. Shear failure
3. Deflection failure
1. Bending failure: Bending failure generally occurs due to
crushing of compression flange or fracture of tension flange of
the beam.
2. Shear failure: This occurs due to buckling of web of the beam
near location of high shear forces. The beam can fail locally
due to crushing or buckling of the web near the reaction of
concentrated loads.
3. Deflection failure: A beam designed to have adequate strength
may become unsuitable if it is not able to support its load
without excessive deflections.
MODES OF FAILURE
61. CONSIDERATIONS IN DESIGN OF BEAMS
• Beams should be proportioned for strength in bending
keeping in view of the lateral and local stability of the
compression flange.
• The selected shape should have capacity to withstand
essential strength in shear and local bearing .
• The beam dimension should be suitably proportioned for
stiffness, keeping in mind their deflections and deformations
under service conditions .
62. LIMITATIONS OF ANGLES , T-SECTIONS AND
CHANNELS
• Angles and T-sections are weak in bending.
• Channels only be used for light loads.
• The rolled steel channels and angle sections are used in those
cases where they can be designed and executed satisfactory.
• This is because the load is not likely to be in the plane, which
removes torsional eccentricities .
• Also, it is complicated to calculate the lateral buckling
characteristics of these sections .