15-Bending Coefficient (Steel Structural Design & Prof. Shehab Mourad)

•

4 likes•3,609 views

This document discusses the bending coefficient Cb, which accounts for the effect of different moment gradients on lateral-torsional buckling. Cb is equal to 1.0 for a uniform moment diagram, representing the worst case for compression flange buckling. The document provides an equation to calculate Cb based on the maximum moment and moments at quarter, half, and three-quarter points of an unbraced beam segment. It also lists some typical Cb values for different support conditions and load types. Finally, it addresses beam shear strength, noting the shear resistance factor and requirement that factored shear strength exceeds factored shear load.

1 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Where, M max : is the largest moment in an unbraced segment
MA, MB & MC: are the moments at the 1/4, 1/2 & 3/4 point in the
segment, respectively.
Bending Coefficient (Cb)
Cb is a moment coefficient to account for the effect of different
moment gradients on lateral - torsional buckling
Cb = 1.0 for a uniform moment diagram
Which represent the worst case
of compression flange buckling,
resulting in the least beam moment resistance
In general, Cb = 12.5 M max
2.5 M max + 3 M A + 4 MB + 3 MC
+
M M
MA
MB = Mmax
MC
Lb = L
1/4 Lb 1/4 Lb 1/4 Lb 1/4 Lb
Compression flang is laterally
supported at ends only , Cb = 1.14
Lb = L/2 Lb = L/2
1/4 Lb 1/4 Lb 1/4 Lb 1/4 Lb
MA
Mmax
MB
MC
Compression flang is laterally
supported at mid span , Cb = 1.30

2 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Some typical values of Cb for different type of loading and different points of
laterally supported compression flange

3 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Beam shear strength
Shear resistance factor ( f v) = 0.90
LRFD strength requirement : f v Vn ≥ Vu
Area of web, Aw = d tw

This document discusses the design of column base plates to resist both axial loads and bending moments. It provides equations to calculate stresses on the base plate and footing. It then gives an example of designing a base plate for a column supporting an axial load of 1735 kN and bending moment of 200 kN.m. The design process involves calculating eccentricity, base plate dimensions, stresses on the footing, required plate thickness, and checking bending in two directions. The example concludes by specifying a base plate of dimensions 750mm x 500mm x 40mm that satisfies all design requirements.

Chapter 12

Afgaab Cumar

The document provides derivations of design equations for reinforced concrete beams. It begins by deriving the equation for maximum moment capacity of a singly reinforced beam based on concrete strength as M=0.167*fck*b*d^2. It then derives equations for doubly reinforced beams where compression steel is also required. The document further derives equations for design of flanged beams depending on whether the neutral axis lies within the flange or web. It concludes by outlining design procedures for singly and doubly reinforced beams.

Structure analysis ii ce331 pdf

Saqib Imran

This document provides an introduction to the moment distribution method for analyzing statically indeterminate structures. It defines key terms like fixed end moments, member stiffness factors, joint stiffness factors, and distribution factors. The method is described as a repetitive process that begins by assuming each joint is fixed, then unlocking and locking joints in succession to distribute moments until joint rotations are balanced. Examples are provided to illustrate how to calculate member stiffness factors based on geometry and applied loads, and how to determine distribution factors by considering a rigid joint connected to members and satisfying equilibrium. The goal of the method is to directly calculate end moments through successive approximations rather than first solving for displacements.

Lec11 Continuous Beams and One Way Slabs(1) (Reinforced Concrete Design I & P...

Hossam Shafiq II

The document discusses reinforced concrete continuity and analysis methods for continuous beams and one-way slabs. It describes how steel reinforcement must extend through members to provide structural continuity. The ACI/SBC coefficient method of analysis is summarized, which uses coefficient tables to determine maximum shear forces and bending moments for continuous beams and one-way slabs under various loading conditions in a simplified manner compared to elastic analysis. Requirements for applying the coefficient method include having multiple spans with ratios less than 1.2, prismatic member sections, and live loads less than 3 times dead loads.

Beam Deflection Formulae

Muhammad Fatkhurrozi

1. The document provides formulas for calculating slope, deflection, and maximum deflection for various beam types under different loading conditions. It gives the equations for cantilever beams with concentrated loads, uniformly distributed loads, and varying loads. It also provides the equations for simply supported beams with these different load types and with couple moments applied. The equations relate the beam properties like length, load location, and intensity to the resulting slope and deflection values.

Isolated column footing

kamariya keyur

This document discusses the design of an isolated column footing, including: 1) Types of isolated column footings and factors that influence footing size like bearing capacity of soil. 2) Key sections to check for bending moment, shear, and development length. 3) Reinforcement requirements. 4) An example problem where a rectangular isolated sloped footing is designed for a column carrying an axial load of 2000 kN. Design checks are performed for footing size, bending moment, shear, development length, and reinforcement.

Analysis of T-Beam

01008828934

1) The document discusses the analysis of flanged beam sections like T-beams and L-beams. It covers topics like effective flange width, positive and negative moment regions, and ACI code provisions for estimating effective flange width. 2) Examples are provided for analyzing a T-beam and an L-beam section. This includes calculating the effective flange width, checking steel strain, minimum reinforcement requirements, and computing nominal moments. 3) Reinforcement limitations for flange beams are also outlined, covering requirements for flanges in compression and tension.

Design of Beam for Shear

illpa

The document discusses shear design of beams. It covers shear strength, which depends on the web thickness and h/t ratio to prevent shear buckling. Shear strength is calculated as 60% of the tensile yield stress. Block shear failure is also discussed, where the strength is governed by the shear and net tension areas. An example calculates the maximum reaction based on block shear for a coped beam connection.

This document provides an introduction to plastic theory for the analysis of structures. It discusses key concepts like the idealized stress-strain curve, assumptions of plastic theory, formation of plastic hinges, and the concept of shape factor. Shape factor is the ratio of the plastic moment capacity to the elastic moment capacity of a cross-section. Several examples are provided to demonstrate calculating shape factors for different cross-sections, including rectangular, I-sections, unsymmetrical sections, and diamond-shaped sections.

Plastic analysis

Shubham Babar

This seminar discusses plastic analysis, which is used to determine the collapse load of structures. It introduces key concepts like plastic hinges, which form at locations of maximum moment and allow large rotations. The plastic section modulus and shape factor are presented as ways to calculate the moment capacity of a fully yielded cross-section. Common collapse mechanisms like simple beams, fixed beams under uniform and point loads, and propped cantilevers are analyzed using the static method of plastic analysis or virtual work method. Determining collapse loads for various structural configurations is demonstrated through examples.

Shear Force And Bending Moment Diagram For Frames

Amr Hamed

Eccentric Loading In Welded Connections

Abhishek Kansara

This document discusses welded connections that experience eccentric loading. It describes two types of eccentrically loaded connections: those that cause twisting moments and those that cause bending moments. For connections with twisting moments, the document explains how to calculate the direct shear stress, torsional stress, and resultant stress. For connections with bending moments, it provides equations to calculate the direct shear stress, bending stress, and resultant stress for both fillet and groove welds. Finally, it includes two examples problems that demonstrate how to analyze and design eccentrically loaded welded connections.

Classification of cross section

Valmik Mahajan

This document discusses the classification of steel cross sections according to Indian Standard IS 800:2007. It explains that cross sections are classified into four classes - plastic, compact, semi-compact, and slender - based on their width-thickness ratio and ability to develop plastic hinges and plastic moment capacity. Formulas and limiting ratios for each class are provided. Three example cross sections are then classified - a ISHB 400 section is compact, a ISMC 300 section is plastic, and a ISA 150X150X12 angle section is semi-compact.

Structural engineering i

Shekh Muhsen Uddin Ahmed

Structural engineering i- Dr. Iftekhar Anam Structural Stability and Determinacy,Axial Force, Shear Force and Bending Moment Diagram of Frames,Axial Force, Shear Force and Bending Moment Diagram of Multi-Storied Frames,Influence Lines of Beams using Müller-Breslau’s Principle,Influence Lines of Plate Girders and Trusses,Maximum ‘Support Reaction’ due to Wheel Loads,Maximum ‘Shear Force’ due to Wheel Loads,Calculation of Wind Load,Seismic Vibration and Structural Response http://www.uap-bd.edu/ce/anam/

Design of steel beams

Ir. David Puen

This document provides an overview of the design of steel beams. It discusses various beam types and sections, loads on beams, design considerations for restrained and unrestrained beams. For restrained beams, it covers lateral restraint requirements, section classification, shear capacity, moment capacity under low and high shear, web bearing, buckling, and deflection checks. For unrestrained beams, it discusses lateral torsional buckling, moment and buckling resistance checks. Design procedures and equations for determining effective properties and capacities are also presented.

Preliminary design of column

ila vamsi krishna

Singly Reinforce Concrete

guest00bb06

Topic1_Method of Virtual Work.pptx

Mary Joanne Aniñon

Portal and cantilever method

Prionath Roy

Approximate analysis methods make simplifying assumptions to determine preliminary member forces and dimensions for indeterminate structures. Case 1 assumes diagonals cannot carry compression and shares shear between diagonals. Case 2 allows compression in diagonals. Portal and cantilever methods analyze frames by dividing into substructures at assumed hinge locations, solving each sequentially from top to bottom.

Beam design

Mohamed Azeem Nijamdeen

This document provides an overview of design in reinforced concrete according to BS 8110. It discusses the basic materials used - concrete and steel reinforcement - and their properties. It describes two limit states for design: ultimate limit state considering failure, and serviceability limit state considering deflection and cracking. Key aspects of beam design are summarized, including types of beams, design for bending and shear resistance, and limiting deflection. Reinforcement detailing rules are also briefly covered.

Structural Design

Vj NiroSh

This document provides design calculations for structural elements of a concrete car park structure according to BS-8110, including: 1. A one-way spanning roof slab with a span of 2.8m, designed as simply supported with 10mm main reinforcement bars at 300mm spacing and 8mm secondary bars. 2. A load distribution beam D and non-load bearing beam E, with calculations provided for beam D's dead and imposed loads. 3. Requirements include individual work submission by January 2nd, 2016 and assumptions to be clearly stated.

Rc corbel example

mamilli

This document summarizes the design of a single reinforced concrete corbel according to ACI 318-05. The corbel is 300mm wide and 500mm deep with 35MPa concrete and 415MPa steel reinforcement. It was designed to resist a vertical load of 370kN applied 100mm from the face of the column. The design includes checking the vertical load capacity, calculating the required shear friction and main tension reinforcement, and designing the horizontal reinforcement. The provided reinforcement of 3 No.6 bars for tension and 3 No.3 link bars at 100mm spacing was found to meet all design requirements.

Lec06 Analysis and Design of T Beams (Reinforced Concrete Design I & Prof. Ab...

Hossam Shafiq II

1) T-beams are commonly used structural elements that can take two forms: isolated precast T-beams or T-beams formed by the interaction of slabs and beams in buildings. 2) The analysis and design of T-beams considers the effective flange width provided by slab interaction or the dimensions of an isolated precast flange. 3) Two methods are used to analyze T-beams: assuming the stress block is in the flange and using rectangular beam theory, or using a decomposition method if the stress block extends into the web.

Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)

Hossam Shafiq II

This document discusses shear in reinforced concrete beams. It covers shear stress and failure modes, shear strength provided by concrete and steel stirrups, design according to code provisions, and critical shear sections. Key points include: transverse loads induce shear stress perpendicular to bending stresses; shear failure is brittle and must be designed to exceed flexural strength; nominal shear strength comes from concrete and steel stirrups according to code equations; design requires checking section adequacy and providing minimum steel area and maximum stirrup spacing. Critical shear sections for design are located a distance d from supports.

AS4100 Steel Design Webinar Worked Examples

ClearCalcs

Basics of Foundation Engineering هندسة الأساسات & Eng. Ahmed S. Al-Agha

Hossam Shafiq II

Basics of Foundation Engineering هندسة الأساسات & Eng. Ahmed S. Al-Agha ------------------------------------------------------------------------------------ Chapter (2) Subsoil Exploration Chapter (3) Ultimate Bearing Capacity of Shallow Foundations Chapter (4) Ultimate Bearing Capacity of Shallow Foundations (Special Cases) Chapter (5) Allowable Bearing Capacity and Settlement Chapter (6) Geometric Design of Shallow Foundations Chapter (7) Lateral Earth Pressure Chapter (8) Retaining Walls Chapter (9) Sheet Pile Walls Chapter (11) Pile Foundations

Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...

Hossam Shafiq II

This chapter discusses truss bridges. It begins by defining a truss as a triangulated assembly of straight members that can be used to replace girders. The main advantages of truss bridges are that primary member forces are axial loads and the open web system allows for greater depth. The chapter then describes the typical components of a through truss bridge and the most common truss forms including Pratt, Warren, curved chord, subdivided, and K-trusses. Design considerations like truss depth, economic spans, cross section shapes, and wind bracing are covered. The chapter concludes with sections on determining member forces, design principles, and specific design procedures.

What's hot

Design of rectangular beam by USD

Sadia Mahjabeen

Design of column base plates anchor bolt

Khaled Eid

Plastic Analysis

Aayushi5

Analysis of beam by plastic theory-part-I,

Subhash Patankar

Plastic analysis

Shubham Babar

Shear Force And Bending Moment Diagram For Frames

Amr Hamed

Eccentric Loading In Welded Connections

Abhishek Kansara

Classification of cross section

Valmik Mahajan

Structural engineering i

Shekh Muhsen Uddin Ahmed

Design of steel beams

Ir. David Puen

Preliminary design of column

ila vamsi krishna

Singly Reinforce Concrete

guest00bb06

Topic1_Method of Virtual Work.pptx

Mary Joanne Aniñon

Portal and cantilever method

Prionath Roy

Beam design

Mohamed Azeem Nijamdeen

Structural Design

Vj NiroSh

Rc corbel example

mamilli

Lec06 Analysis and Design of T Beams (Reinforced Concrete Design I & Prof. Ab...

Hossam Shafiq II

Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)

Hossam Shafiq II

AS4100 Steel Design Webinar Worked Examples

ClearCalcs

What's hot (20)

Design of rectangular beam by USD

Design of column base plates anchor bolt

Plastic Analysis

Analysis of beam by plastic theory-part-I,

Plastic analysis

Shear Force And Bending Moment Diagram For Frames

Eccentric Loading In Welded Connections

Classification of cross section

Structural engineering i

Design of steel beams

Preliminary design of column

Singly Reinforce Concrete

Topic1_Method of Virtual Work.pptx

Portal and cantilever method

Beam design

Structural Design

Rc corbel example

Lec06 Analysis and Design of T Beams (Reinforced Concrete Design I & Prof. Ab...

Lec09 Shear in RC Beams (Reinforced Concrete Design I & Prof. Abdelhamid Charif)

AS4100 Steel Design Webinar Worked Examples

More from Hossam Shafiq II

Basics of Foundation Engineering هندسة الأساسات & Eng. Ahmed S. Al-Agha

Hossam Shafiq II

Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...

Hossam Shafiq II

Ch7 Box Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metw...

Hossam Shafiq II

1. Box girder bridges have two key advantages over plate girder bridges: they possess torsional stiffness and can have much wider flanges. 2. For medium span bridges between 45-100 meters, box girder bridges offer an attractive form of construction as they maintain simplicity while allowing larger span-to-depth ratios compared to plate girders. 3. Advances in welding and cutting techniques have expanded the structural possibilities for box girders, allowing for more economical designs of large welded units.

Ch6 Composite Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Pr...

Hossam Shafiq II

Ch5 Plate Girder Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Me...

Hossam Shafiq II

Plate girders are commonly used as main girders for short and medium span bridges. They are fabricated by welding together steel plates to form an I-shape cross-section, unlike hot-rolled I-beams. Plate girders offer more design flexibility than rolled sections as the plates can be optimized for strength and economy. However, their thin plates are more susceptible to various buckling modes which control the design. Buckling considerations of the compression flange, web in shear and bending must be evaluated to determine the plate girder's load capacity.

Ch4 Bridge Floors (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally ...

Hossam Shafiq II

This chapter discusses bridge floors for roadway and railway bridges. It describes three main types of structural systems for roadway bridge floors: slab, beam-slab, and orthotropic plate. For railway bridges, the two main types are open timber floors and ballasted floors. The chapter then covers design considerations for allowable stresses, stringer and cross girder cross sections, and provides an example design for the floor of a roadway bridge with I-beam stringers and cross girders.

Ch3 Design Considerations (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. M...

Hossam Shafiq II

This chapter discusses design considerations for steel bridges. It outlines two main design philosophies: working stress design and limit states design. The chapter then focuses on the working stress design method, which is based on the Egyptian Code of Practice for Steel Constructions and Bridges. It provides allowable stress values for various steel grades and loading conditions, including stresses due to axial, shear, bending, compression and tension loads. Design of sections is classified based on compact and slender criteria. The chapter also addresses stresses from repeated, erection and secondary loads.

Ch2 Design Loads on Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr....

Hossam Shafiq II

This document discusses design loads on bridges. It describes various types of loads that bridges must be designed to resist, including dead loads from the bridge structure itself, live loads from traffic, and environmental loads such as wind, temperature, and earthquakes. It provides specifics on how to calculate loads from road and rail traffic according to Egyptian design codes, including truck and train configurations, impact factors, braking and centrifugal forces, and load distributions. Other loads like wind, thermal effects, and concrete shrinkage are also summarized.

Ch1 Introduction (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally A...

Hossam Shafiq II

This document provides an introduction to steel bridges, including: 1. It discusses the history and evolution of bridge engineering and the key components of bridge structures. 2. It describes different classifications of bridges according to materials, usage, position, and structural forms. The structural forms include beam bridges, frame bridges, arch bridges, cable-stayed bridges, and suspension bridges. 3. It provides examples of different types of bridges and explains the basic structural systems used in bridges, including simply supported, cantilever, and continuous beams as well as rigid frames.

Lec05 STRUCTURE SYSTEMS to resist EARTHQUAKE (Earthquake Engineering هندسة ال...

Hossam Shafiq II

Lec04 Earthquake Force Using Response Specturum Method (2) (Earthquake Engine...

Hossam Shafiq II

Lec03 Earthquake Force Using Response Specturum Method (1) (Earthquake Engine...

Hossam Shafiq II

Lec02 Earthquake Damage to Concrete Structure (Earthquake Engineering هندسة ا...

Hossam Shafiq II

Lec01 Design of RC Structures under lateral load (Earthquake Engineering هندس...

Hossam Shafiq II

Lec13 Continuous Beams and One Way Slabs(3) Footings (Reinforced Concrete Des...

Hossam Shafiq II

Lec12 Continuous Beams and One Way Slabs(2) Columns (Reinforced Concrete Desi...

Hossam Shafiq II

Lec10 Bond and Development Length (Reinforced Concrete Design I & Prof. Abdel...

Hossam Shafiq II

This document discusses bond and development length in reinforced concrete. It defines bond as the adhesion between concrete and steel reinforcement, which is necessary to develop their composite action. Bond is achieved through chemical adhesion, friction from deformed bar ribs, and bearing. Development length refers to the minimum embedment length of a reinforcement bar needed to develop its yield strength by bonding to the surrounding concrete. The development length depends on factors like bar size, concrete strength, bar location, and transverse reinforcement. It also provides equations from design codes to calculate the development length for tension bars, compression bars, bundled bars, and welded wire fabric. Hooked bars can be used when full development length is not available, and the document discusses requirements for standard hook geome

Lec07 Analysis and Design of Doubly Reinforced Beam (Reinforced Concrete Desi...

Hossam Shafiq II

Lec05 Design of Rectangular Beams with Tension Steel only (Reinforced Concret...

Hossam Shafiq II

The document discusses design considerations for rectangular reinforced concrete beams with tension steel only. It covers topics such as beam proportions, deflection control, selection of reinforcing bars, concrete cover, bar spacing, effective steel depth, minimum beam width, and number of bars. Beam proportions should have a depth to width ratio of 1.5-2 for normal spans and up to 4 for longer spans. Minimum concrete cover and bar spacings are specified to protect the steel. Effective steel depth is the distance from the extreme compression fiber to the steel centroid. Design assumptions must be checked against the final design.

Lec04 Analysis of Rectangular RC Beams (Reinforced Concrete Design I & Prof. ...

Hossam Shafiq II

This document discusses the ultimate flexural analysis of reinforced concrete beams according to building codes. It covers topics such as concrete stress-strain relationships, stress distributions at failure, nominal and design flexural strength, moments in beams, tension steel ratios, minimum steel requirements, ductile and brittle failure modes, and calculations for balanced and maximum steel ratios. Diagrams illustrate key concepts regarding stress blocks, strain distributions, and section types. Formulas are presented for determining balanced steel ratio, maximum steel ratio, and checking neutral axis depth.

More from Hossam Shafiq II (20)