18-Beam Column Strength (Steel Structural Design & Prof. Shehab Mourad)

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1. The document discusses second order effects (P-Δ effects) on beam-column members subjected to axial forces and bending moments. It defines magnification factors B1 and B2 that account for P-Δ effects for braced and unbraced members, respectively. 2. Equations are provided for calculating the ultimate moment Mu for braced (Mu = B1*Mnt) and unbraced (Mu = B2*Mlt) members based on the primary moments and magnification factors. 3. Two strength equations are given for designing beam-column members based on the column and beam design strengths and accounting for P-Δ effects on the ultimate moments and axial load.

1 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Beam – Column Strength
- Second order effect ( P - D)
Effect of axial force on members having deformations due to
transversal or lateral loading
If the member is braced at ends;
Mnt = is the primary moment due to
transverse loads
d co = deformation due to transverse load
d c = deformation of member due to
transverse loading and axial load
M u = Mnt + Pu . d c
= B1 . Mnt
Where, B1 is a moment magnification factor for a braced member
If the member is unbraced ;
M lt = is the primary moment resulted from sway
D = lateral deflection due to sway
M u = M lt + P . D
= B2 . M lt
Where, B2 is a moment magnification factor for a unbraced member
Therefore for a general member, the final moment taking into
consideration second order effect will be in the form
M u = B1 . Mnt + B2 . M lt
Pu Pu
dcodc
Deflection after P was applied
Deflection before P was applied
dco
w u
Pu
L
Pu
M nt = wL2
/8
Primary Moment Mnt, If P = 0
PuD
Pu
M u
Secondary moment
for braced case
Secondary moment
for unbraced case

2 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Where, B1 = Cm ³ 1.0
1 - ( Pu / Pe1)
C m : factor accounts for type of loading and member – end moments
P e1 : Euler buckling load of the member = p2
E I / (KL)2
where, I & L for the axis of bending and (K) for a braced member
For beam-column not subjected to transverse loads
Cm = 0.60 – 0.4 M1
M2
Where;
M1: is the absolute value of smaller moment at
end
M2 : is the absolute value of larger moment at
end
and M1/M2 = - ve for single curvature
= + ve for double curvature
For beam-column subjected to transverse loads
Cm is given as in the shown table

3 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Where, B2 = 1 ³ 1.0
1 - ∑ Pu
∑ Pe2
Strength Equations for Beam – Column
1) when Pu ³ 0.20
f Pn
Pu + 8 Mux + Muy £ 1.0
f Pn 9 f Mnx f Mny
2) when Pu < 0.20
f Pn
Pu + Mux + Muy £ 1.0
2 f Pn f Mnx f Mny
where;
f Pn : Column design strength (obtained from column strength)
f Mnx : Beam design strength about x-x axis (obtained from beam strength)
f Mny: Beam design strength about y-y axis (obtained from beam strength)
Pu : Ultimate column load (obtained from factored loads)
Mux : Ultimate bending moment about x-x axis
(obtained from factored loads with the second order effects)
Muy : Ultimate bending moment about y-y axis
(obtained from factored loads with the second order effects)
∑ Pu = Pu1 + Pu2 + Pu3
Where, ∑ Pu is the summation of all ultimate
loads of columns in a story of frame
And, ∑ Pe2 is the summation of Euler buckling
load of all columns in the frame,
where Pe2 = p2
E I / (KL)2
where, I & L for the axis of bending and (K)
for a unbraced member

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

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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

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.

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

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.

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

Hossam Shafiq II

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