17-Examples of Beams (Steel Structural Design & Prof. Shehab Mourad)

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1. A steel beam with a 9m span is designed to support uniform loads. The lightest W-shape sections are selected for different cases of lateral support of the top flange. 2. For full lateral support, a W610x82 section is selected. For support at 2.25m intervals, the same section satisfies strength requirements. 3. A W610x92 section is required for support at mid-span. 4. A W460x128 section satisfies strength and deflection limits for no lateral support.

1 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Examples on beam design
A simple steel beam (A36) has a span of 9m and is supporting a uniform service dead
load = 12 kN/m and service live load = 21 kN/m,
Find the lightest W- Shape section for the following Cases :
1) The top flange in laterally supported continuously with RC Slab
2) The top flange is supported at (2.25m) apart
3) The top flange is only supported at mid span
4) The top flange is supported at only ends.
Solution:-
Fy = 250 MPa
wult = 1.2 D + 1.6 L = 1.2 x 12 + 1.6 x 21 = 48 kN/m
Mult max = wL2
/8 = 48 (9)2
/8 = 486 kN.m
Qult max = w L /2 = 48 x 9 /2 = 216 kN
Case 1:
Top flange is continuously laterally supported .
Lb = 0 < Lp
Look for the lightest W- Shape , so that
Ø Mp > 486 kN.m (Zone 1) of curve
From LRFD tables Choose W 610 x 82
Mp= 495 kN.m , Lp= 1.7m, L r = 4.99 m BF= 57.8
For zone 1 of curve
ØMp= Fy.Zx = 495 kN.m
Ø Mn least of
Ø 1.5 Fy Sx =0.9(1.5) 250 x 1870x103
x 10-6
= 631.12 kN.m
Therefore Ø Mn = 495 kN.m > M ult max = 486 kN.m
W 610 x 82 is Safe
486 kN.m
+
+
-
216 k N
216 k N
w
L = 9 m

2 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Check shear strength
For W 610 x 82 h = 534 mm , tw = 10 mm, d = 599 mm
h = 534 = 53.4
tw 10
2.45 E = 2.45 2x 105
= 69.30 , h < 2.45 E
Fy 250 tw Fy
Ø Vn= (0.90) 0.6 x 250 x (599 x 10) x 10-3
= 808.65 kN > Vult = 216 kN
The W 610 x 82 section is Safe in shear
Case 2
Top flange is laterally @ 2.25m Lb=2.25m
Try to use same section W 610x82
Mp= 495 kN.m , Lp= 1.7m, Lr = 4.99 m, BF= 57.8
Lb> Lp beam is located in zone 2 on curve
Therefore, Ø Mn = Cb [Ø Mp – BF (L b - L p) ]
Check for part 2 of beam :-
Cb2 = 12.5 M max
2.5 Mmax+ 3MA+4MB+3MC
Cb2 = 12.5 x 486 = 1.061
2.5 x 486 + 3 x 417.7 + 4 x 455.6 + 3 x 478.4
The factored resistance of W 610x82, for Lb = 2.25 m
Ø Mn = 1.061 [495 - 57.8 (2.25-1.70) ] = 491.46 kN. m < Ø Mp= 495 kN.m
Ø Mn = 491.46 kN.m > Mult max = 486 kN.m
Lb= 2.25 Lb= 2.25
Critical part, Cb in
less, and maximum
moment is applied
417.7
455.6
478.4
486
364.5
W610 x 82 is safe for unsupported length of compression flange = 2.25 m

3 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Case 3 : Top flange is laterally supported at mid span (4.5m)
Lb = 4.5m and most probably will be greater than Lp
Therefore the beam is located at zone 2 of beam curve
Cb = 12.5 Mmax
2.5M max + 3MA + 4MB + 3Mc
Cb = 12.5 x 486 = 1.30
2.5 x 486 + 3 x 212.6 + 4 x 364.5 + 3 x 455.6
Enter beam graphs and look for the lightest section with,
Lb=4.5 m, and factored resistance not less than Mmax / Cb = 458/1.30 = 373.8 kN.m
From graph, the lightest section is W 610 x 92
From beam tables, for W 610 x 92, Ø Mp= 565 kN.m , Lp = 1.74 m, BF = 62.1
Ø Mn = 1.30 [ 565 -62.1( 4.5-1.74)] = 511.68 < 565 kN.m
Ø Mn= 511.68 kN.m > M ult max = 486 kN.m
Case 4 : The top flange is only laterally supported at ends
Lb= 9m.
Cb = 12.5x486 = 1.136
2.5 x 486 + 3 x 364.5 + 4 x 486 +3x364.56
Look for a lightest section in zone 2 in beam graphs, with Lb =9.0 m,
With a factored resistance not less than Mmax / Cb = 486 /1.136 = 427.7 kN.m
From graph choose, W 460 x 128,
From Tables Ø Mp = 686 kN.m , Ø Mr = 445 kN.m, Lp = 3.33 m , Lr = 10.8 m, BF = 32.3
Ø Mn = 1.136 [ 686 -32.3 (9-3.33)] = 571 kN.m < Ø Mp
Ø Mn = 571 kN.m. > M ult max = 486 kN.m
MA =364.5 MC = 364.5
MB= M max =486
Lb= 9.00
MB =364.5
MC = 455.6
M max =486
MA = 212.6
Lb= 4.50 Lb= 4.50
W 610 x 92 is Safe for Lb= 4.50 m
W 460 x 128 is Safe for Lb= 9.0 m

4 Prepared by Prof. Shehab Mourad – Department of Civil Eng. - KSU
Check deflection due to live load W 460 x 128
From W-shape tables , Ix = 6.37x108
mm4
E = 2 x 105
MPa (N/mm2
)
L = 9000 mm
Service live load = w = 21 kN/m = 21x1000 N = 21 N /mm
1000 mm
For uniform load on simply supported beam, the max deflection = 5 w L 4
384 EI
r max = 5 x 21 x (9000)4
= 14.09 mm
384 x 2 x 105
x 6.37 x 108
r all = L = 9000 = 25 mm
360 360
r max < r all
W 460 x 128 satisfies the deflection limits as well as strength requirements for
unsupported compression flange = 9.0 m

1. The document provides examples of checking the strength of beams and columns. 2. In the first example, the beam section W 310 x 97 is checked to resist ultimate loads and is found to be safe. 3. In the second example, the safety of column section W 360 x 72 is checked for a given load of 250 kN when laterally supported at mid-height. It is found to be unsafe by about 8% and requires a larger section.

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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.

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

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

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.

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