Bending Element Definition
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Symbols
Cb : The lateral-torsional buckling modification factor defined by Equation 9.1
E: Modulus of elasticity of steel = 29,000 ksi (200 000 MPa)
Fy : Specified minimum yield stress of the type of steel being used, ksi
Its : Effective radius of gyration
J: Torsion constant
ho : Distance between the flange centroids, in. (mm)
Lb : Length between points that are either braced against the lateral displacement of the compression flange or braced against twist of the cross-section, in. (mm)
Lp : The limiting laterally unbraced length for the limit state of yielding, in. (mm)
Lr : The limiting unbraced length for the limit state of inelastic lateral-torsional buckling, in. (mm),
Mn : The nominal flexural strength
Mp : Plastic flexural moment
Wpx : Plastic section modulus is taken about the x-axis in.3 (mm3)
Wex : Elastic section modulus is taken about the x-axis, in.3 (mm3)
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Bending Member Definition
These are elements that are under the effect of a simple bending flexural moment around any of their principal axes. In For the elements that are under the effect of the simple bendingflexural moment, the loads should act be acting in the plane parallel to the principal axis passing through the shear center or the element should be supported against torsion at the load impact application points and supports.
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Yielding Limit State
It is a situation where the cross-section of the beam is dimensioned to remain stable until it becomes plastic plasticize under the effect of bending, flexure if the local buckling of the pressure head compression flange and the lateral twisting buckling is prevented. In this case, the characteristic moment strength can be taken equal to the plastic moment strength.
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The yield moment is the moment value when the uppermost fiber of the section under the influence effect of bending flexural moment reaches the yield stress.
Plastic Moment is the moment value when all fibers of the section under the effect of bending flexural moment reach the yield stress.
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Lateral Torsional Buckling Limit State
The part of the beam in the pressure head area that is under the compression acts like an axially loaded pressure compression bar. If the stability of the pressure head compression flange is not sufficient, the beam section cannot reach its full bending flexural capacity. In this case, similar to the pressure compression elements; General buckling or loss of stability in cross-sectional parts that may occur with local buckling determines the collapse limit state. This type of buckling of the pressure head compression flange is called lateral torsion buckling.
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Design with ÇYTHYE 2018
9.2.1
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Yielding Limit State
The characteristic bending flexural moment strength Mn for the yield limit state is calculated by equation 9.2.
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For the lateral torsion buckling limit state, the characteristic bending moment strength is divided for 3 different failure limit conditions, which are the laterally unsupported unbraced length of the pressure head compression part Mn, the change changes that occur due to Lb and the effect of the moment correction coefficient Cb are shown in the figure below.:
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a) If Lb ≤ Lp, this limit situation need not be taken into account.
b) If Lp <Lb ≤ Lr, the characteristic bending flexural moment strength Mn is calculated by equation 9.3.
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c) If Lb > Lr, the characteristic bending flexural moment strength Mn shall be determined by equation 9.4.
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Cb Coefficient: It is the positive contribution of bending flexural moment propagation distribution along the length between the supporting points supported by the lateral stability connection in for the case of lateral-torsional buckling limit.
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Design
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for Combined
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Forces
It is the The strength calculation is made by taking into account the combined stresses created in the elements members under bending a flexural moment and axial force.
Account Computational details are available at Birleşik Etki Altında Tasarım Design of Steel Members for Combined Forces.
Icons
C b : Moment correction coefficient defined by Equation 9.1
E: Structural steel modulus of elasticity
F y : Structural steel characteristic yield stress
I ts : Effective radius of inertia
J: Torsion constant
h o : Distance between center of gravity of cross section heads (= d -tf)
L b : Element length between the points where lateral displacement and cross-section twisting in the pressure head are prevented
L p : Laterally unsupported boundary length for the flow limit state
L r : Limit length in non-elastic lateral twist sprain
M n : Characteristic bending moment strength
M p : Plastic bending moment
W px : plastic strength moment about the x-axis
W ex : moment of elastic strength around the x-axis
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