This document provides formulas and examples for calculating torsional section properties of steel shapes, including the St. Venant torsional constant, warping torsional constant, shear centre location, and monosymmetry constant. It covers open cross sections like W-shapes, channels, angles, and T-sections, as well as closed hollow structural sections that are round or square/rectangular. Simple examples are given to illustrate the calculations.
This document discusses different types of power transmission elements including couplings, clutches, and brakes. It describes various coupling types such as rigid couplings (sleeve, clamp, and flange) and flexible couplings (bushed pin type flange, universal, and Oldham). Friction and positive contact clutches are examined along with examples like disc, cone, and centrifugal friction clutches and jaw positive contact clutches. Finally, common brake types are defined including block, band, internal expanding shoe, and disc brakes.
ME 312 Mechanical Machine Design is the flagship course of the mechanical engineering department at DHA Suffa University. This lecture is about mechanical fasteners and non-permanent joints. The course is offered every fall by Dr. Bilal A. Siddiqui.
The document discusses concepts related to shear force and bending moment in beams, including:
- Definitions of bending, beams, planar bending, and types of beams including simple, cantilever, and overhanging beams.
- Calculation sketches simplify beams, loads, and supports for analysis.
- Internal forces in bending include shear force and bending moment. Relations and diagrams relate these to external loads.
- Equations define shear force and bending moment at each beam section. Diagrams illustrate variations along the beam.
This document provides an overview of torsion and power transmission in shafts. It defines the torsion equation that relates torque, shear stress, polar second moment of area, and angle of twist. Formulas are derived for solid and hollow circular shafts. Examples are provided to calculate shear stress, angle of twist, and maximum torque or power given various shaft properties and limitations. The document also relates mechanical power to torque and rotational speed.
This document outlines standards and procedures for determining loads on silo and tank structures from stored bulk materials. It includes definitions of terms and symbols, methods for calculating fill and discharge loads on silo walls, loads in silo hoppers and bottoms, and loads on tanks. Measurement procedures are provided for determining important bulk material parameters needed for load calculations, such as density, wall friction, internal friction, and elasticity. Annexes provide additional guidance, standards, and alternative calculation methods.
IRJET- Design and Fabrication of Manual Roller Bending MachineIRJET Journal
This document describes the design and fabrication of a manual roller bending machine. The machine uses a roller mechanism powered by a manually operated spindle wheel to bend metal strips. It has a supporting frame to hold the roller assembly. One roller is connected to the spindle wheel via a chain drive mechanism to power it. A movable center roller can be adjusted using a screw mechanism to control the bending angle. The machine is designed to be portable and affordable while reducing human effort during operation. Design calculations are provided for components like the chain drive, power screw, and required bending forces and torques for different metal thicknesses. Dimensions and a 3D model of the machine are also presented. Testing showed the machine can successfully bend metal strips but takes more
Taper roller bearings are used in a variety of industrial applications. They consist of an inner ring, outer ring, and tapered rollers. Proper installation is important for long life and performance. Bearings must be carefully fitted and mounted, ensuring correct tolerances, preload, and lubrication to transfer loads efficiently.
This document discusses different types of power transmission elements including couplings, clutches, and brakes. It describes various coupling types such as rigid couplings (sleeve, clamp, and flange) and flexible couplings (bushed pin type flange, universal, and Oldham). Friction and positive contact clutches are examined along with examples like disc, cone, and centrifugal friction clutches and jaw positive contact clutches. Finally, common brake types are defined including block, band, internal expanding shoe, and disc brakes.
ME 312 Mechanical Machine Design is the flagship course of the mechanical engineering department at DHA Suffa University. This lecture is about mechanical fasteners and non-permanent joints. The course is offered every fall by Dr. Bilal A. Siddiqui.
The document discusses concepts related to shear force and bending moment in beams, including:
- Definitions of bending, beams, planar bending, and types of beams including simple, cantilever, and overhanging beams.
- Calculation sketches simplify beams, loads, and supports for analysis.
- Internal forces in bending include shear force and bending moment. Relations and diagrams relate these to external loads.
- Equations define shear force and bending moment at each beam section. Diagrams illustrate variations along the beam.
This document provides an overview of torsion and power transmission in shafts. It defines the torsion equation that relates torque, shear stress, polar second moment of area, and angle of twist. Formulas are derived for solid and hollow circular shafts. Examples are provided to calculate shear stress, angle of twist, and maximum torque or power given various shaft properties and limitations. The document also relates mechanical power to torque and rotational speed.
This document outlines standards and procedures for determining loads on silo and tank structures from stored bulk materials. It includes definitions of terms and symbols, methods for calculating fill and discharge loads on silo walls, loads in silo hoppers and bottoms, and loads on tanks. Measurement procedures are provided for determining important bulk material parameters needed for load calculations, such as density, wall friction, internal friction, and elasticity. Annexes provide additional guidance, standards, and alternative calculation methods.
IRJET- Design and Fabrication of Manual Roller Bending MachineIRJET Journal
This document describes the design and fabrication of a manual roller bending machine. The machine uses a roller mechanism powered by a manually operated spindle wheel to bend metal strips. It has a supporting frame to hold the roller assembly. One roller is connected to the spindle wheel via a chain drive mechanism to power it. A movable center roller can be adjusted using a screw mechanism to control the bending angle. The machine is designed to be portable and affordable while reducing human effort during operation. Design calculations are provided for components like the chain drive, power screw, and required bending forces and torques for different metal thicknesses. Dimensions and a 3D model of the machine are also presented. Testing showed the machine can successfully bend metal strips but takes more
Taper roller bearings are used in a variety of industrial applications. They consist of an inner ring, outer ring, and tapered rollers. Proper installation is important for long life and performance. Bearings must be carefully fitted and mounted, ensuring correct tolerances, preload, and lubrication to transfer loads efficiently.
This document provides an overview and analysis of torsion in structural steel members. It discusses torsional fundamentals such as shear centers and resistance to torsional moments. It also covers general torsional theory, analysis of torsional stresses, specification provisions, and design examples. Appendices include tables of torsional properties, graphs of torsional functions, and supporting information on torsional analysis.
This document provides a concise summary of Eurocode 2 (EC2) for the design of reinforced concrete framed buildings. It aims to guide readers through the key aspects of EC2 and other relevant Eurocodes. The publication covers topics such as basis of design, materials, durability, structural analysis, bending and axial load, shear, punching shear, torsion, serviceability, detailing requirements, and design aids. It is intended to help designers transition to designing according to EC2 and the UK National Annex.
Unit 4 Design of Power Screw and Screw JackMahesh Shinde
The document discusses power screws, including their terminology, types of threads, torque analysis, and efficiency. It defines key terms like nominal diameter, pitch, lead, and lead angle. It describes common types of threads like square, ACME, and buttress threads. It discusses torque required to raise and lower loads, including expressions for self-locking and overhauling screws. The document also covers screw efficiency and collar friction torque, providing expressions to calculate overall efficiency. An example calculation is given to find maximum load lifted, efficiency, and overall efficiency of a screw jack.
This document describes how to use Mohr's circle to analyze stresses in a stressed material. Mohr's circle provides a graphical representation of the relationships between normal and shear stresses on inclined planes. It can be used to calculate principal stresses, maximum shear stresses, and stresses on inclined planes. The document includes several numerical examples showing how to construct and use Mohr's circles to solve for these values given known stresses and orientations in a material.
c'est un power point qui parle sur les roulements et ses utilisation en pratique dans le mechanic ainsi les charge qu'il faut considerer lors d'assemblage
DESIGN OF A MODEL HAULAGE TECHNIQUE FOR WATER FLOODING CAISSON ASSEMBLY.Emeka Ngwobia
Presented in this study is the engineering solution to the movement of a 63m, 45tons Caisson from a fabrication yard to a field location in the Gulf of guinea. This was achieved by dividing the whole process into three stages; firstly by using excel sheets with relevant design formulas to design the spreader bar configuration to lift the caisson from the quayside to a crane barge conveniently, showing the necessary lifting sequence employed to complete this process, also designing the lifting accessories needed which includes pad eyes, shackles, wire rope and spreader bars according to relevant codes and standards The first spreader Is an I beam of length of 25m and section with dimension 533mm by 229mm weighing 129kg/m, the second beam and the third beam are designed similarly as an I beam of length 9m and section 533mm by 229mm weighing 129kg/m. The choice of pad eye to be welded on the spreader beam was based on the working limit of the pad eye, which was analytically designed using spread sheet, performing necessary checks to make sure it will not break off during the lifting operations. It is reinforced with cheek plates at the pin hole to reduce the stresses at the pin hole. The total pad eye used for this operation is 16. The choice of shackle attached to each of the pad eye was based on the total self weight of all the lifting materials(55tons), according to the Crosby group catalogue it is an S2130 bow shackle of Nominal size 50.8mm, Stock no 1019659 and weight 23.7002kg, also the wire rope configuration chosen to based on the safe working load limit according to the Bethlehem wire rope general purpose catalogue ASME B30.5- 1995 the wire rope has nominal strength of 53.1tons, sling class 19x7 IWRC(Purple or extra improved ploy (EIP Steel).
. Secondly, by providing solutions to sea fastening for the caisson on the deck of the crane barge, which was modeled using STAADPRO, which involved support designs and loss of support designs, so as to accommodate for the hydrodynamic effect while the caisson is being transported by the crane barge, having in mind that the crane barge chosen will adequately accommodate the caisson because of the deck space required to fit the 63m long caisson, from the analysis the Caisson is supported by steel beams spaced at 10 m interval which is fastened with the aid of a clamp as seen in the detailed drawings, this caisson and beam supports are modeled with staadpro software and support reactions obtained. These supports are now spaced at 20 m intervals and analyzed to simulate a situation where there is a loss of support reaction during transportation of the caisson. A saddle clamp is to joined to a H beam for support to hold it to the deck at varying length and at the starting point a pivot made from a pad eye joined with a pin to connect the saddle clamp to allow for easy lifting of the caisson when it is at 25m to the FPSO.
ic Engine and reciprocating machine ch1.pdfTsegayePaulos1
The document provides an overview of internal combustion (IC) engines and their components. It discusses how IC engines work and are classified. Specifically, it notes that IC engines convert the chemical energy of fuel into thermal energy and use this to produce mechanical work. It also outlines the basic components of IC engines like the cylinder block, cylinder head, pistons, valves/ports, camshaft, crankshaft, and connecting rod. Furthermore, it explains the four stroke cycle of intake, compression, power, and exhaust strokes and compares it to the two stroke cycle which completes the process in two strokes. Terminology used in IC engines is also defined.
5 beams- Mechanics of Materials - 4th - BeerNhan Tran
This document contains chapter 5 from the textbook "Mechanics of Materials" which discusses the analysis and design of beams for bending. It includes introductions to shear and bending moment diagrams, sample problems calculating reactions and drawing the diagrams, relationships between load, shear and bending moment, and considerations for designing prismatic beams for bending. The key concepts covered are determining internal shear forces and bending moments, using equilibrium to draw shear and bending moment diagrams, and selecting beam cross sections based on required section modulus and allowable stresses.
Cahier de cours de génie mécanique pour les élèves de la quatrième année sciences techniques. Ce cahier est proposé par Mr Mtaallah Mohamed, Enseignant de génie mécanique au lycée secondaire AbdelAziz Khouja à Kélibia, Tunisie.
This document provides information about moment of inertia including:
- Definitions of terms like center of gravity, radius of gyration, section modulus, and moment of inertia.
- Formulas for calculating moment of inertia of basic geometric sections and symmetrical/unsymmetrical sections about various axes.
- Examples of finding the center of gravity and moment of inertia of different cross-sections like rectangles, circles, T-sections, and L-sections.
Design of Machine Elements 2 mark Question and Answersbaskaransece
This document provides information on the design of machine elements including shafts, keys, and couplings. It begins with definitions of key terms like factor of safety and design processes. It then discusses loads, stresses, materials selection factors. Specific topics covered include types of shafts and stresses on shafts, standard shaft sizes, hollow vs solid shafts, keys and keyways, couplings, and manufacturing methods for shafts.
This section will introduce how to solve problems of axially loaded members such as stepped and tapered rods loaded in tension. The concept of strain energy will also be introduced.
This document provides an overview and analysis of torsion in structural steel members. It discusses torsional fundamentals such as shear centers and resistance to torsional moments. It also covers general torsional theory, analysis of torsional stresses, specification provisions, and design examples. Appendices include tables of torsional properties, graphs of torsional functions, and supporting information on torsional analysis.
This document provides a concise summary of Eurocode 2 (EC2) for the design of reinforced concrete framed buildings. It aims to guide readers through the key aspects of EC2 and other relevant Eurocodes. The publication covers topics such as basis of design, materials, durability, structural analysis, bending and axial load, shear, punching shear, torsion, serviceability, detailing requirements, and design aids. It is intended to help designers transition to designing according to EC2 and the UK National Annex.
Unit 4 Design of Power Screw and Screw JackMahesh Shinde
The document discusses power screws, including their terminology, types of threads, torque analysis, and efficiency. It defines key terms like nominal diameter, pitch, lead, and lead angle. It describes common types of threads like square, ACME, and buttress threads. It discusses torque required to raise and lower loads, including expressions for self-locking and overhauling screws. The document also covers screw efficiency and collar friction torque, providing expressions to calculate overall efficiency. An example calculation is given to find maximum load lifted, efficiency, and overall efficiency of a screw jack.
This document describes how to use Mohr's circle to analyze stresses in a stressed material. Mohr's circle provides a graphical representation of the relationships between normal and shear stresses on inclined planes. It can be used to calculate principal stresses, maximum shear stresses, and stresses on inclined planes. The document includes several numerical examples showing how to construct and use Mohr's circles to solve for these values given known stresses and orientations in a material.
c'est un power point qui parle sur les roulements et ses utilisation en pratique dans le mechanic ainsi les charge qu'il faut considerer lors d'assemblage
DESIGN OF A MODEL HAULAGE TECHNIQUE FOR WATER FLOODING CAISSON ASSEMBLY.Emeka Ngwobia
Presented in this study is the engineering solution to the movement of a 63m, 45tons Caisson from a fabrication yard to a field location in the Gulf of guinea. This was achieved by dividing the whole process into three stages; firstly by using excel sheets with relevant design formulas to design the spreader bar configuration to lift the caisson from the quayside to a crane barge conveniently, showing the necessary lifting sequence employed to complete this process, also designing the lifting accessories needed which includes pad eyes, shackles, wire rope and spreader bars according to relevant codes and standards The first spreader Is an I beam of length of 25m and section with dimension 533mm by 229mm weighing 129kg/m, the second beam and the third beam are designed similarly as an I beam of length 9m and section 533mm by 229mm weighing 129kg/m. The choice of pad eye to be welded on the spreader beam was based on the working limit of the pad eye, which was analytically designed using spread sheet, performing necessary checks to make sure it will not break off during the lifting operations. It is reinforced with cheek plates at the pin hole to reduce the stresses at the pin hole. The total pad eye used for this operation is 16. The choice of shackle attached to each of the pad eye was based on the total self weight of all the lifting materials(55tons), according to the Crosby group catalogue it is an S2130 bow shackle of Nominal size 50.8mm, Stock no 1019659 and weight 23.7002kg, also the wire rope configuration chosen to based on the safe working load limit according to the Bethlehem wire rope general purpose catalogue ASME B30.5- 1995 the wire rope has nominal strength of 53.1tons, sling class 19x7 IWRC(Purple or extra improved ploy (EIP Steel).
. Secondly, by providing solutions to sea fastening for the caisson on the deck of the crane barge, which was modeled using STAADPRO, which involved support designs and loss of support designs, so as to accommodate for the hydrodynamic effect while the caisson is being transported by the crane barge, having in mind that the crane barge chosen will adequately accommodate the caisson because of the deck space required to fit the 63m long caisson, from the analysis the Caisson is supported by steel beams spaced at 10 m interval which is fastened with the aid of a clamp as seen in the detailed drawings, this caisson and beam supports are modeled with staadpro software and support reactions obtained. These supports are now spaced at 20 m intervals and analyzed to simulate a situation where there is a loss of support reaction during transportation of the caisson. A saddle clamp is to joined to a H beam for support to hold it to the deck at varying length and at the starting point a pivot made from a pad eye joined with a pin to connect the saddle clamp to allow for easy lifting of the caisson when it is at 25m to the FPSO.
ic Engine and reciprocating machine ch1.pdfTsegayePaulos1
The document provides an overview of internal combustion (IC) engines and their components. It discusses how IC engines work and are classified. Specifically, it notes that IC engines convert the chemical energy of fuel into thermal energy and use this to produce mechanical work. It also outlines the basic components of IC engines like the cylinder block, cylinder head, pistons, valves/ports, camshaft, crankshaft, and connecting rod. Furthermore, it explains the four stroke cycle of intake, compression, power, and exhaust strokes and compares it to the two stroke cycle which completes the process in two strokes. Terminology used in IC engines is also defined.
5 beams- Mechanics of Materials - 4th - BeerNhan Tran
This document contains chapter 5 from the textbook "Mechanics of Materials" which discusses the analysis and design of beams for bending. It includes introductions to shear and bending moment diagrams, sample problems calculating reactions and drawing the diagrams, relationships between load, shear and bending moment, and considerations for designing prismatic beams for bending. The key concepts covered are determining internal shear forces and bending moments, using equilibrium to draw shear and bending moment diagrams, and selecting beam cross sections based on required section modulus and allowable stresses.
Cahier de cours de génie mécanique pour les élèves de la quatrième année sciences techniques. Ce cahier est proposé par Mr Mtaallah Mohamed, Enseignant de génie mécanique au lycée secondaire AbdelAziz Khouja à Kélibia, Tunisie.
This document provides information about moment of inertia including:
- Definitions of terms like center of gravity, radius of gyration, section modulus, and moment of inertia.
- Formulas for calculating moment of inertia of basic geometric sections and symmetrical/unsymmetrical sections about various axes.
- Examples of finding the center of gravity and moment of inertia of different cross-sections like rectangles, circles, T-sections, and L-sections.
Design of Machine Elements 2 mark Question and Answersbaskaransece
This document provides information on the design of machine elements including shafts, keys, and couplings. It begins with definitions of key terms like factor of safety and design processes. It then discusses loads, stresses, materials selection factors. Specific topics covered include types of shafts and stresses on shafts, standard shaft sizes, hollow vs solid shafts, keys and keyways, couplings, and manufacturing methods for shafts.
This section will introduce how to solve problems of axially loaded members such as stepped and tapered rods loaded in tension. The concept of strain energy will also be introduced.
This document provides an introduction and overview of Corus Advance structural sections for use in steel construction. It includes the following key points:
- Corus is a major UK and global steel producer and manufacturer of structural steel sections.
- Steel construction offers benefits like speed of construction, economy, flexibility, sustainability, and recyclability.
- The document contains selection of structural section property tables from the Corus Advance range to assist students in steel structure design.
- For the full listing of Advance section properties and capacities, the online "Blue Book" can be downloaded from the Corus website.
15. beam analysis using the stiffness methodChhay Teng
1. The document discusses analyzing beams using the stiffness method. It introduces node coordinates and degrees of freedom, and defines member stiffness matrices for individual beam elements.
2. It provides examples of applying the method to simple structures like trusses and slider mechanisms by assembling the element stiffness matrices into a global stiffness matrix.
3. The method relates displacements at nodes to applied forces using the member stiffness matrices. This allows solving for unknown displacements given known forces or vice versa.
This chapter discusses brickwork materials and construction techniques. Bricks are one of the oldest man-made building materials, dating back over 4000 years. Bricks are typically made from clay but can also contain sand, lime, or cement. Common types of bricks include clay bricks, fly ash bricks and kiln-burnt bricks. Mortar is used to join bricks and consists of cement, sand and water. There are various bonding patterns used in brickwork such as stretcher bond, header bond and Flemish bond. Equipment used includes trowels, jointers, spirit levels and bricklayers' tools. Proper construction techniques such as joint spacing, bonding and laying patterns are important for quality and durable brickwork.
The document provides instructions for carpentry works. It discusses 1) planning works which includes preparing drawings, considering safety measures and allocating tasks. 2) woodworking such as sawing, planing and wood joints. 3) metal works including welding and metal cutting. 4) masonry including bricklaying. 5) painting procedures and types of paint. 6) plastering works. 7) scaffolding erection and types of scaffolding. The document provides detailed guidance on various carpentry techniques and ensuring work quality and safety.
This document provides an overview of structural engineering topics including:
1. Loads on structures such as dead loads, service loads, and wind loads. Stress and strain, Hooke's law, and Poisson's ratio as they relate to structural analysis.
2. Soil and foundation engineering including soil mechanics, subsurface exploration methods, soil sampling, and field testing. Shallow and deep foundations as well as foundation excavation methods.
3. Reinforced concrete including cementitious materials, aggregates, concrete admixtures, forming and placing concrete, curing concrete, and inspection. Design of common concrete elements such as slabs, beams, walls, and foundations.
4. Structural steel construction including design of tension
11. displacement method of analysis slope deflection equationsChhay Teng
1. The document discusses the displacement method of analysis known as the slope-deflection method. This method analyzes the deformations of structures using slope-deflection equations.
2. General procedures for the displacement method are described, including determining degrees of freedom and establishing slope-deflection equations for each member.
3. Slope-deflection equations relate the displacements (rotations and translations) of joints to member end actions (moments and shears). These equations allow determining member forces based on known joint displacements.
A.matrix algebra for structural analysisdocChhay Teng
The document provides definitions and examples of different types of matrices including matrix algebra, matrix operations, and properties of matrix operations. It defines matrices, matrix types (square, identity, symmetric, triangular), and matrix operations including addition, subtraction, scalar multiplication, and matrix multiplication. Matrix multiplication involves multiplying the rows of the first matrix with the columns of the second matrix. The properties discussed are that matrix multiplication is noncommutative, distribution over addition holds, and distribution over matrix multiplication holds.
This document discusses materials and application of Portland cement plaster. Key points:
1. Portland cement plaster consists of cement, aggregate, lime and water. It is used for exterior and interior finishing.
2. Recommended materials include Portland cement, sand, lime and water. Admixtures can be added to improve workability.
3. Application involves mixing, applying in coats, and curing. A three-coat application provides the best finish.
This summary highlights the main components, materials, and application process for Portland cement plaster in 3 sentences.
This document discusses the selection and design of standard steel beams and columns. It provides information on:
1) How to select standard steel sections from reference tables that list section properties like elastic section modulus.
2) How to calculate required section modulus based on maximum bending moment and allowable stress.
3) Guidelines for selecting sections, including choosing sections that minimize weight for beams and have slenderness ratios below 180 for columns.
4) An example of designing a simply supported beam by calculating bending moment, allowable stress, and required section modulus.
1. The presentation covered design for torsion in structural members, including definitions, effects of torsion such as rotation and warping, and methods for calculating torsional stresses.
2. Equations were presented for calculating torsional moments in circular and rectangular beams under different loading cases.
3. Two theories for analyzing reinforced concrete members under torsion were discussed: skew bending theory and space truss analogy theory. Limitations on torsional reinforcement in concrete were also reviewed.
This document provides an overview of basic design considerations for machine components. It discusses general design procedures and considerations, types of loads, stress-strain diagrams, types of stresses including tensile, compressive, shear, crushing, bearing, torsional, and bending stresses. It also covers concepts related to stress concentration, creep, fatigue, endurance limit, factor of safety, and theories of failure under static loads. Standard classifications and designations of various steel and alloy types are also presented.
The document provides an overview of mechanics of materials concepts related to torsion, including:
- Torsion causes shearing stresses that vary linearly from zero at the center to a maximum at the surface for circular shafts.
- Torsion can cause both shearing stresses and normal stresses depending on the orientation of the material element.
- Ductile materials fail in shear while brittle materials fail in tension when subjected to torsion.
- The angle of twist is proportional to the applied torque, material properties, and shaft length based on elastic torsion formulas.
- Stress concentrations can occur due to geometric discontinuities and influence the maximum shearing stress.
The document discusses guidelines for detailing reinforcement in concrete structures. It begins by defining detailing as the preparation of working drawings showing the size and location of reinforcement. Good detailing ensures reinforcement and concrete interact efficiently. The document then discusses sources of tension in concrete structures from various loading conditions like bending, shear, and connections. It provides equations from AS3600-2009 for calculating minimum development lengths for reinforcing bars to develop their yield strength based on bar size, concrete strength, and transverse reinforcement. It also discusses lap splice requirements. In summary, the document provides best practice guidelines for detailing reinforcement to efficiently resist loads and control cracking in concrete structures.
Reinforced concrete II Hand out Chapter 5_PPT_Torsion.pdfObsiNaanJedhani
This document discusses torsion in reinforced concrete beams. It describes:
- How torsional stresses develop and are distributed in circular, rectangular, and thin-walled hollow members. The maximum stress occurs at the surface.
- Cracking and failure occur due to principal tensile stresses at 45 degrees, forming spirals. Torsion reinforcement controls cracking.
- An equivalent space truss model is used to design for torsion, with stirrups resisting shear across cracks like tension members and longitudinal bars as chords.
- Equations are provided to calculate required torsional reinforcement and the maximum torque before crushing of the concrete.
This document discusses concepts related to the design of concrete beams including:
1. It introduces concepts like bending, shear, tension and compression as they relate to beam design.
2. It provides formulas for calculating reactions, shear forces, and bending moments in simply supported beams under different loading conditions.
3. It explains concepts like the neutral axis, stress blocks, and strain diagrams that are important to beam design.
4. It discusses factors that influence the strength of beams like the moment of inertia and reinforcement ratio.
5. It compares working stress and limit state methods of design.
This document provides guidance on permissible stress levels for various types of welds, including complete and partial penetration groove welds, fillet welds, and plug and slot welds. It specifies the permissible stress levels for welds under different loading conditions such as tension, compression, shear, and fatigue. It also provides a table matching weld metal strength levels to common base metal grades. The document is intended to help engineers properly design welded connections and determine required weld sizes.
This document discusses various topics related to stresses and failure theories in machine elements. It defines notations used for stress analysis and provides formulas to calculate torsional shear stress, bending stress in straight and curved beams, principal stresses under bi-axial loading, and maximum stresses based on different failure theories. Examples are also presented on topics like torsion, shafts in series/parallel, bending stresses, and determination of principal stresses. Theories of failure under static load for ductile and brittle materials are described based on yield point and ultimate stresses from tension tests.
The document discusses torsion and stresses in circular shafts. It covers topics like net torque due to internal stresses, shear components, shaft deformations, stresses in the elastic range, failure modes, and examples of solving for stress and deformation in statically determinate and indeterminate shafts made of elastic and elastoplastic materials. Sample problems are included to demonstrate calculating stresses, strains, and required diameters for various shaft configurations under applied torques.
The document discusses steel structures and structural drafting. It covers various topics related to steel including properties, structural joints, technical terms, and design elements. Specific sections are dedicated to steel columns, plate girders, purposes and uses of steel, advantages and disadvantages of steel structures, steel structure drawings, working drawings, fabrication, and roof systems of steel trusses. The document provides information needed for structural drafting and elementary structural design.
Analysis and Design of Reinforced Concrete Beamsc4ppuc1n0
The document discusses the behavior of reinforced concrete beams under flexure. It covers the basic assumptions in flexure theory including plane sections remaining plane, equal strains in concrete and steel, and modeling the concrete stress-strain relationship. It also discusses the stress block model used to calculate flexural strength and provides examples of calculating the centroid and moment of inertia for uncracked and cracked beam sections. The examples show how cracking causes the centroid to shift upward and the moment of inertia to decrease significantly.
IRJET - An Investigation of Stresses Induced in Curved Beams using MATLAB...IRJET Journal
This document investigates stresses induced in curved beams using MATLAB and finite element analysis (FEA). It analyzes three cross-sectional shapes - trapezoidal, circular, and elliptical - for a crane hook subjected to a 100kN load. MATLAB code is used to calculate stresses in each section, finding the trapezoidal section experiences the lowest maximum stress of 171 MPa. FEA software ANSYS is also used to model each section and determine von Mises stresses, validating the results. The trapezoidal section is identified as optimal for withstanding the load with minimum induced stress.
This document discusses stresses that occur at the junction between cylindrical shells and conical bottoms or ends in pressure vessels. It presents an analysis of the compression stresses that exist in this area and provides equations and tables to calculate the stresses. The author proposes allowable stress values and provides guidance on reinforcing thickness requirements to safely address the stresses at the cylinder-cone junction.
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.
The document discusses the conjugate beam method for analyzing beams. It begins by defining the conjugate beam method and explaining that the load on the conjugate beam is equal to the bending moment diagram of the real beam divided by EI. It provides examples of how to determine the supports and loading of the conjugate beam based on the real beam. It then gives the procedure for using the method to find the slope and deflection at any point on the real beam, which involves solving the conjugate beam for reactions and cutting at the desired point to get the shear and moment values. Finally, it provides an example problem demonstrating the full procedure.
Comparative Study on Anchorage in Reinforced Concrete Using Codes of Practice...IJERA Editor
This paper (Part II) reports a comparative study for BS8110 and EC2 of practice and those expressions by Batayneh and Neilsen on tests from literature. These have been treated under straight bar anchorages with transverse pressure. The aim of this study is to evaluate the reliability of the existing equations for bond strength of straight bars by applying to the available tests in the literature .The most important parameters were examined in these tests are concrete strength, anchorage length, concrete covers, bar diameter and transverse pressure. 264 tests from the literature have been chosen, which are all for straight bars with transverse pressure. The specimens are pull-out specimens with small concrete covers, beams ends and slabs. For both comparative studies in Part I and Part II, the conclusions and recommendations are presented here together.
Design methods for torsional buckling of steel structuresBegum Emte Ajom
The document discusses methods for designing steel structures to resist torsional buckling. It summarizes clauses from Eurocode 3 that provide equations for calculating the elastic critical buckling moment and determining the reduction factor used to calculate the design bending strength. It also presents simplified equations that can be used to calculate the elastic critical buckling moment for common steel beam sections. Additional guidance is provided for calculating the critical buckling moment for non-symmetric sections and when bending occurs about the major axis.
This document provides information about flexural testing of materials including steel, pine, and Douglas fir. It includes the experimental setup, procedures, formulas used to calculate flexural properties, graphs of load vs deformation, and tables of test data for each material. The key results are the ultimate flexural strengths of 2.2 kips for steel, 1.05 kips for pine, and still to be determined for Douglas fir. Comparisons are made between the flexural properties of the different materials.
2009 ncdd-csf-technical-manual-vol-i-study-design-guidelinesChhay Teng
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2. Introduction
Structural engineers occasionally need to determine the section properties of steel shapes not
found in the current edition of the Handbook of Steel Construction (CISC 2000). The following
pages provide the formulas for calculating the torsional section properties of structural steel
shapes.
The section properties considered are the St. Venant torsional constant, J, the warping
torsional constant, Cw, the shear centre location, yO , and the monosymmetry constant, βx .
Also included are the torsional constant, C, and the shear constant, CRT, for hollow structural
sections (HSS). Although not a torsional section property, the shear constant is included
because it is not easily found in the literature.
Some of the formulas given herein are less complex than those used in developing the
Handbook and the Structural Section Tables (CISC 1997). Effects such as flange-to-web fillet
radii, fillet welds, and sloped (tapered) flanges have not been taken into account. Likewise,
some of the formulas for monosymmetric shapes are approximations which are only valid
within a certain range of parameters. If needed, more accurate expressions can be found in
the references cited in the text.
Simple example calculations are provided for each type of cross section to illustrate the
formulas. A complete description of torsional theory or a detailed derivation of the formulas for
torsional section properties is beyond the scope of this discussion; only the final expressions
are given. The references can be consulted for further information.
Although no effort has been spared in an attempt to ensure that all data contained herein is
factual and that the numerical values are accurate to a degree consistent with current
structural design practice, the Canadian Institute of Steel Construction does not assume
responsibility for errors or oversights resulting from the use of the information contained
herein. Anyone making use of this information assumes all liability arising from such use. All
suggestions for improvement will receive full consideration.
2 CISC 2002
3. St. Venant Torsional Constant
The St. Venant torsional constant, J, measures the resistance of a structural member to pure
or uniform torsion. It is used in calculating the buckling moment resistance of laterally
unsupported beams and torsional-flexural buckling of compression members in accordance
with CSA Standard S16.1-94 (CSA 1994).
For open cross sections, the general formula is given by Galambos (1968):
b′ t 3
J = ∑
3
[1]
where b' are the plate lengths between points of intersection on their axes, and t are the plate
thicknesses. Summation includes all component plates. It is noted that the tabulated values in
the Handbook of Steel Construction (CISC 2000) are based on net plate lengths instead of
lengths between intersection points, a mostly conservative approach.
The expressions for J given herein do not take into account the flange-to-web fillets. Formulas
which account for this effect are given by El Darwish and Johnston (1965).
For thin-walled closed sections, the general formula is given by Salmon and Johnson (1980):
2
4 AO
J= [2]
∫ S
ds t
where AO is the enclosed area by the walls, t is the wall thickness, ds is a length element
along the perimeter. Integration is performed over the entire perimeter S.
3 CISC 2002
4. Warping Torsional Constant
The warping torsional constant, Cw, measures the resistance of a structural member to
nonuniform or warping torsion. It is used in calculating the buckling moment resistance of
laterally unsupported beams and torsional-flexural buckling of compression members in
accordance with CSA Standard S16.1-94 (CSA 1994).
For open sections, a general calculation method is given by Galambos (1968). For sections in
which all component plates meet at a single point, such as angles and T-sections, a
calculation method is given by Bleich (1952). For hollow structural sections (HSS), warping
deformations are small, and the warping torsional constant is generally taken as zero.
Shear Centre
The shear centre, or torsion centre, is the point in the plane of the cross section about which
twisting takes place. The shear centre location is required for calculating the warping torsional
constant and the monosymmetry constant. It is also required to determine the stabilizing or
destabilizing effect of gravity loading applied below or above the shear centre, respectively
(SSRC 1998). The coordinates of the shear centre location (xO, yO) are calculated with
respect to the centroid. A calculation method is given by Galambos (1968).
Monosymmetry Constant
The monosymmetry constant, βX, is used in calculating the buckling moment resistance of
laterally unsupported monosymmetric beams loaded in the plane of symmetry (CSA 2000). In
the case of a monosymmetric section that is symmetric about the vertical axis, the general
formula is given by SSRC (1998):
∫ y (x )
1
βX = 2
+ y 2 dA − 2 y O [3]
IX A
where IX is moment of inertia about the horizontal centroidal axis, dA is an area element and
yO is the vertical location of the shear centre with respect to the centroid. Integration is
performed over the entire cross section. The value of βX is zero for doubly-symmetric
sections.
4 CISC 2002
5. HSS Torsional Constant
The torsional constant, C, is used for calculating the shear stress due to an applied torque. It
is expressed as the ratio of the applied torque, T, to the shear stress in the cross section, τ :
T
C= [4]
τ
HSS Shear Constant
The shear constant, CRT, is used for calculating the maximum shear stress due to an applied
shear force.
For hollow structural sections, the maximum shear stress in the cross section is given by:
VQ
τ max = [5a]
2t I
where V is the applied shear force, Q is the statical moment of the portion of the section lying
outside the neutral axis taken about the neutral axis, I is the moment of inertia, and t is the
wall thickness.
The shear constant is expressed as the ratio of the applied shear force to the maximum shear
stress (Stelco 1981):
V 2t I
C RT = = [5b]
τ max Q
5 CISC 2002
6. A) Open Cross Sections
1. Doubly-Symmetric Wide-Flange Shapes (W-Shapes and I-Beams)
Fig. 1a Fig. 1b
Torsional section properties (flange-to-web fillets neglected):
2 b t 3 + d ′w 3
J= (Galambos 1968) [6]
3
Cw =
(d ′)2 b 3 t (Galambos 1968, Picard and Beaulieu 1991) [7]
24
d′ = d − t [8]
Example calculation: W610x125
d = 612 mm, b = 229 mm, t = 19.6 mm, w = 11.9 mm
d' = 592 mm
J = 1480 x 103 mm4
Cw = 3440 x 109 mm6
6 CISC 2002
7. 2. Channels
Fig. 2a Fig. 2b
Torsional section properties (flange slope and flange-to-web fillets neglected):
2 b′ t 3 + d ′ w 3
J= (SSRC 1998) [9]
3
3 1 − 3 α α2 d ′ w
C w = (d ′) (b ′) t
2
+ 1 +
(Galambos 1968, SSRC 1998) [10]
6 2 6 b ′ t
1
α= [11]
d ′w
2+
3 b′ t
d′ = d − t , b′ = b − w 2 [12]
Shear centre location:
w
xo = x + b′ α − (Galambos 1968, Seaburg and Carter 1997) [13]
2
Example calculation: C310x31
d = 305 mm, b = 74 mm, t = 12.7 mm, w = 7.2 mm
(Actual flange slope = 1/6; zero slope assumed here for simplicity)
d' = 292 mm, b' = 70.4 mm
J = 132 x 103 mm4
α = 0.359, Cw = 29.0 x 109 mm6
x = 17.5 mm (formula not shown)
xO = 39.2 mm
7 CISC 2002
8. 3. Angles
Fig. 3a Fig. 3b
Torsional section properties (fillets neglected):
J=
(d ′ + b ′)t 3 [14]
3
Cw =
t3
36
[ ]
(d ′)3 + (b′)3 (Bleich 1952, Picard and Beaulieu 1991) [15]
t t
d′ = d − , b′ = b − [16]
2 2
The warping constant of angles is small and often neglected. For double angles, the values of
J and Cw can be taken equal to twice the value for single angles.
The shear centre (xO, yO) is located at the intersection of the angle leg axes.
Example calculation: L203x102x13
d = 203 mm, b = 102 mm, t = 12.7 mm
d' = 197 mm, b' = 95.7 mm
J = 200 x 103 mm4
Cw = 0.485 x 109 mm6
8 CISC 2002
9. 4. T-Sections
Fig. 4a Fig. 4b
Torsional section properties (flange-to-web fillets neglected):
b t 3 + d ′w 3
J= [17]
3
b 3 t 3 (d ′) w 3
3
Cw = + (Bleich 1952, Picard and Beaulieu 1991) [18]
144 36
t
d′ = d − [19]
2
The warping constant of T-sections is small and often neglected.
The shear centre is located at the intersection of the flange and stem plate axes.
Example calculation: WT180x67
d = 178 mm, b = 369 mm, t = 18.0 mm, w = 11.2 mm
d' = 169 mm
J = 796 x 103 mm4
Cw = 2.22 x 109 mm6
9 CISC 2002
10. 5. Monosymmetric Wide-Flange Shapes
Fig. 5a Fig. 5b
Torsional section properties (fillet welds neglected):
b1 t 1 + b2 t 2 + d ′ w 3
3 3
J= (SSRC 1998) [20]
3
(d ′)2 b13 t 1 α
Cw = (SSRC 1998, Picard and Beaulieu 1991) [21]
12
1
α= [22]
1 + (b1 b2 ) (t 1 t 2 )
3
(t 1 + t 2 )
d′ = d − [23]
2
Subscripts "1" and "2" refer to the top and bottom flanges, respectively, as shown on Fig. 5b.
Shear centre location:
t1
YO = YT − − α d ′ (Galambos 1968) [24]
2
The sign of YO calculated from Eq. 24 indicates whether the shear centre is located above
(YO > 0) or below (YO < 0) the centroid. The shear centre is generally located between the
centroid and the wider of the two flanges. For doubly-symmetric sections, YO is equal to zero
since the centroid and shear centre coincide.
10 CISC 2002
11. Monosymmetry constant:
I 2 Iy
β X ≈ δ 0.9 (2 ρ − 1) d ′ 1 − y ,
≤ 0.5 (Kitipornchai and Trahair 1980) [25]
Ix
Ix
I y TOP
ρ= = 1− α [26]
Iy
Eq. 25 is an approximate formula and is only valid if IY ≤ 0.5 IX, where IY and IX are the
moments of inertia of the section about the vertical and horizontal centroidal axes,
respectively. A more accurate expression is given by SSRC (1998).
The value of δ depends on which flange is in compression:
+ 1 If the top flange is in compression
δ = [27]
− 1 If the bottom flange is in compression
Generally, the value of βX obtained from Eq. 25 will be positive when the wider flange is in
compression and negative when in tension.
Example calculation: WRF1200x244 The top flange is in compression.
d = 1200 mm, b1 = 300 mm, b2 = 550 mm, t1 = t2 = 20.0 mm, w = 12.0 mm
d' = 1180 mm
α = 0.860, ρ = 1 - α = 0.140
J = 2950 x 103 mm4
Cw = 53 900 x 109 mm6
YT = 695 mm (formula not shown)
YO = -330 mm
Since YO is negative, the shear centre is located between the centroid and the bottom flange.
IX = 7240 x 106 mm4, IY = 322 x 106 mm4 (formulas not shown)
IY / IX = 0.0445 < 0.5 OK
δ = +1
βX = -763 mm (The top flange is narrower and in compression.)
11 CISC 2002
12. 6. Wide-Flange Shapes with Channel Cap
Fig. 6a Fig. 6b
Torsional section properties (flange-to-web fillets neglected):
A conservative estimate of the St. Venant torsional constant is given by:
J ≈ JW + JC [28]
The "w" and "c" subscripts refer to the W-shape and channel, respectively. A more refined
expression for J is proposed by Ellifritt and Lue (1998).
Shear centre location:
tW + w C
YO = YT − − a + e (Kitipornchai and Trahair 1980) [29]
2
a = (1 − ρ ) h , b = ρ h [30]
I y TOP I y TOP
ρ= = [31]
I y TOP + I y BOT Iy
where Iy TOP, Iy BOT, and Iy are the moments of inertia of the built-up top flange (channel + top
flange of the W-shape), the bottom flange, and the entire built-up section about the vertical
axis, respectively. With the channel cap on the top flange, as shown on Fig. 6, the value of YO
obtained from Eq. 29 will be positive, indicating that the shear centre is located above the
centroid.
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13. The distance between the shear centres of the top and bottom flanges is given by:
wC
h = dW − tW + +e [32]
2
The distance between the shear centre of the built-up top flange and the centre line of the
channel web and W-shape top flange, taken together as a single plate, is given by:
2 2
bC d C t C
e= [33]
4 ρ Iy
Warping constant of the built-up section:
Cw = a 2 I y TOP + b 2 I y BOT (Kitipornchai and Trahair 1980) [34]
A simplified formula for Cw is also given by Ellifritt and Lue (1998).
Monosymmetry constant:
I 2 b Iy
β X ≈ δ 0.9 (2 ρ − 1) h 1 − y 1 + C ,
I 2d ≤ 0.5 (Kitipornchai and Trahair 1980) [35]
x Ix
where d is the built-up section depth:
d = dW + w C [36]
Eq. 35 is an approximation which is only valid if IY ≤ 0.5 IX, where Ix is the moment of inertia
of the built-up section about the horizontal centroidal axis. See page 11 for the value of δ and
the sign of βX . A further simplified expression is given by Ellifritt and Lue (1998).
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14. Example calculation: W610x125 and C310x31
W-shape: W610x125
dW = 612 mm, bW = 229 mm, tW = 19.6 mm, wW = 11.9 mm
JW = 1480 x 103 mm4 (previously calculated, p. 6)
Channel cap: C310x31
dC = 305 mm, bC = 74 mm, tC = 12.7 mm, wC = 7.2 mm
JC = 132 x 103 mm4 (previously calculated, p. 7)
Built-up section, with the top flange in compression:
J = 1610 x 103 mm4
YT = 255 mm (formula not shown)
Iy TOP = 73.1 x 106 mm4 (formula not shown)
Iy BOT = 19.6 x 106 mm4 (formula not shown)
Iy = 92.7 x 106 mm4
ρ = 0.789
e = 22.1 mm
h = 618 mm
a = 130 mm
b = 488 mm
YO = 134 mm
Since the calculated value of YO is positive, the shear centre is located above the centroid
(see Fig. 6b).
CW = 5900 x 109 mm6
Ix = 1260 x 106 mm4 (formula not shown)
d = 619 mm
Iy / Ix =0.0736 < 0.5 OK
δ = +1 (top flange in compression)
βX = 339 mm (wider top flange in compression)
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15. B) Closed Cross Sections
7. Hollow Structural Sections (HSS), Round
Fig. 7
St. Venant torsional constant (valid for any wall thickness):
J = 2I =
π
32
[d 4
− (d − 2 t )
4
] (Stelco 1981, Seaburg and Carter 1997) [37]
where d is the outer diameter, I is the moment of inertia, and t is the wall thickness. The
warping constant Cw is taken equal to zero.
HSS torsional constant (valid for any wall thickness):
2J
C= (Stelco 1981, Seaburg and Carter 1997) [38a]
d
HSS shear constant:
2t I
C RT = (Stelco 1981) [38b]
Q
I=
π
64
[d 4
− (d − 2 t )
4
] [39]
Q=
t
6
(
3d 2 − 6d t + 4t 2 ) (Stelco 1981) [40]
Example calculation: HSS324x9.5
d = 324 mm, t = 9.53 mm
J = 233 000 x 103 mm4, I = 116 x 106 mm4 , Q = 471 x 103 mm3
C = 1440 x 103 mm3, CRT = 4710 mm2
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16. 8. Hollow Structural Sections (HSS), Square and Rectangular
Fig. 8
St. Venant torsional constant (valid for thin-walled sections, b / t ≥ 10):
2
4 AP t
J≈ (Salmon and Johnson 1980) [41]
p
Mid-contour length:
p = 2 [(d − t ) + (b − t )] − 2 RC (4 − π ) [42]
Enclosed area:
AP = (d − t )(b − t ) − RC (4 − π )
2
[43]
Mean corner radius:
RO + R i
RC = ≈ 1 .5 t [44]
2
where d and b are the longer and shorter outside dimensions, respectively, and t is the wall
thickness. RO and Ri are the outer and inner corner radii taken equal to 2t and t, respectively.
The warping constant Cw is usually taken equal to zero.
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17. HSS torsional constant (valid for thin-walled sections, b / t ≥ 10):
C ≈ 2 t Ap (Salmon and Johnson 1980, Seaburg and Carter 1997) [45a]
HSS shear constant (approximate):
C RT ≈ 2 t (h − 4 t ) (Stelco 1981) [45b]
where h is the outer section dimension in the direction of the applied shear force. A more
accurate expression is also given by Stelco (1981).
Example calculation: HSS203x102x6.4
d = 203 mm, b = 102 mm, t = 6.35 mm
RO = 12.7 mm
Ri = 6.35 mm
RC = 9.53 mm
p = 568 mm
Ap = 18 700 mm2
J = 15 600 x 103 mm4
It is assumed that the shear force acts in a direction parallel to the longer dimension, d.
h = d = 203 mm
C = 238 x 103 mm3
CRT = 2260 mm2
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18. References
Bleich, F. 1952. Buckling Strength of Metal Structures, McGraw-Hill Inc., New York, N.Y.
CISC. 1997. Structural Section Tables (SST Electronic Database), Canadian Institute of Steel
Construction, Willowdale, Ont.
CISC. 2000. Handbook of Steel Construction, 7th Edition, 2nd Revised Printing. Canadian
Institute of Steel Construction, Willowdale, Ont.
CSA. 1994. Limit States Design of Steel Structures. CSA Standard S16.1-94. Canadian
Standards Association, Rexdale, Ont.
CSA. 2000. Canadian Highway Bridge Design Code. CSA Standard S6-00. Canadian
Standards Association, Rexdale, Ont.
El Darwish, I.A. and Johnston, B.G. 1965. Torsion of Structural Shapes. ASCE Journal of the
Structural Division, Vol. 91, ST1.
Errata: ASCE Journal of the Structural Division, Vol. 92, ST1, Feb. 1966, p. 471.
Ellifritt, D.S. and Lue, D.-M. 1998. Design of Crane Runway Beam with Channel Cap.
Engineering Journal, AISC, 2nd Quarter.
Galambos, T.V. 1968. Structural Members and Frames. Prentice-Hall Inc., Englewood Cliffs,
N.J.
Kitipornchai, S. and Trahair, N.S. 1980. Buckling Properties of Monosymmetric I-Beams.
ASCE Journal of the Structural Division, Vol. 106, ST5.
Picard, A. and Beaulieu, D. 1991. Calcul des charpentes d'acier. Canadian Institute of Steel
Construction, Willowdale, Ont.
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19. Salmon, C.G. and Johnson, J.E. 1980. Steel Structures, Design and Behavior, 2nd Edition.
Harper & Row, Publishers. New York, N.Y.
Seaburg, P.A. and Carter, C.J. 1997. Torsional Analysis of Structural Steel Members.
American Institute of Steel Construction, Chicago, Ill.
SSRC. 1998. Guide to Stability Design Criteria for Metal Structures, 5th Edition. Edited by
T.V. Galambos, Structural Stability Research Council, John Wiley & Sons, New York,
N.Y.
Stelco. 1981. Hollow Structural Sections - Sizes and Section Properties, 6th Edition. Stelco
Inc., Hamilton, Ont.
19 CISC 2002