钢结构基本原理课件 (9).ppt

Local Buckling of BeamsBasic Principles of Steel Structures3.3.2 Local Stability of Web 3.3.1 Local Stability of Compression Flange 3.3.3 Design Criteria and Preventive Measure 3.3.1Local Stability of Compression Flange Local stability 1.1.1 1The thickness of flange is much smaller than the height of the cross-section,and the stress gradient along the thickness of the flange is not large.As uniform pressure plate2 2In order to give full play to the strength of the material,a certain thickness of steel plate is used.Make the critical stress cr is more than the yield point of the steel3 3Considering the plasticity of the beam flange,the plastic coefficient is introduced.4 4The method of limiting the width-thickness ratio is adopted to ensure the stability of the compressed flange plate.The general expression of the local instability critical stress：E=2.06105 N/mm2,v=0.3 Local instability critical stress 2.2.(3.29)(3.30)3.3.1Local Stability of Compression Flange 1 1 t is the thickness of the pressure plate,b is the width of the compression plate.2 2 k is the stability factor of the rectangular plate.3.3.1Local Stability of Compression Flange Local instability critical stress 2.2.Fig.3.10 I-section Box-section3 3 For I-section,the value of b is shown in Fig 3.10 a.For Box-section,the value of b is shown in Fig.3.10 b.Box-shape section,k=4.0,=0.25,Width-Thickness Ratio:Elastic design:I-shape flange、T-shape flange and flange of overhanging part of box-shape section.k=0.425,=0.25,=1.0,Width-Thickness Ratio:3.3.1Local Stability of Compression Flange Local instability critical stress 2.2.(3.31)(3.32)(3.33)As shown in Fig.3.11,if the web is simply supported on four sides under pure bending,if the web is too thin,when the bending moment reaches a certain value,the web will bucking under bending compressive stress.Fig.3.11 Web stress distribution Pure bending action 1.1.3.3.2Local Stability of Web (3.34)(3.35)The value of buckling coefficient k depends on the ratio()of the maximum and minimum pressure on the edge of the plate and the length-width ratio()of the plate.The relationship between k value and is as follows：Formula：Pure bending action 1.1.3.3.2Local Stability of Web Fig.3.12 k relation under the action of uneven pressure(3.36a)(3.36b)(3.36c)I-shape section usually has flange thicker than web,which restricts the rotation of web edge.Considering the constraint effect of the flange,multiplied by the elastic embedding coefficient ,when=2.0,=1.61Bring into formula(3.36a):Pure bending action 1.1.3.3.2Local Stability of Web (3.37)As shown in Fig.3.13,the part between the transverse stiffeners of the beam web is a rectangular plate supported on four sides.The four sides are subjected to uniform shear forces and are in a pure shear state.The principal stress in the plate is equal to the shear force at an angle of 45.The principal compressive stress can cause the buckling of the plate,presenting an inclined buckling along about 45,perpendicular to the direction of the principal compressive stress.Fig.3.13 Shear buckling of plates Uniform shear action 2.2.3.3.2Local Stability of Web I-shape section:a and hw replace lmax and lmin,fvy=fy.Substitute into formula(3.29)According to formula(3.29):Embedding coefficient =1.24.lmax lmin Long and short sides of plate.3.3.2Local Stability of Web Uniform shear action 2.2.(3.38)(3.39)(3.40)When unilateral lateral pressure acts.The web may buckling in the area close to the pressure due to large local load or too thin plate(Fig.3.14).In this case,the critical stress is expressed by formula:Fig.3.14 Buckling of plates under unilateral compression C1 is the coefficient related to a/h,and the critical stress unit is N/mm2Unilateral lateral pressure 3.3.3.3.2Local Stability of Web (3.41)I-shape section:tw and hw replace t and h,a/hw=2.C1=166.When the flange size of I-section meets b/t 13 (235/fy),the flange will not Local buckling.1 13.3.2Local Stability of Web Unilateral lateral pressure 3.3.When the Web size hw/tw 84 (235/fy),Single action of shear stress,local compressive stress or bending stress.local buckling of Web will not occur prior to steel yield.2 2when hw/tw 174 (235/fy),Local buckling will not occur under the action of bending moment.4 4(3.42)when hw/tw 104 (235/fy),Local buckling will not occur under the action of shear or bending moment alone.3 3 Under the simultaneous action of uneven pressure on both sides,uniform shear force and lateral pressure on one side:In the actual web of a beam,there are often several stress joint actions at the same time.Under the simultaneous action of uniform pressure on both sides,uniform shear force and lateral pressure on one side:Complex stress action 4.4.3.3.2Local Stability of Web (3.43)(3.44)Critical stress curve under various distributed forces:Fig.3.15 Critical stress curve under various distributed forces3.3.2Local Stability of Web Complex stress action 4.4.Design criteria to ensure local stability 1.1.3.3.3Design criteria and Prevent。