1. Week 3 Flexural members PDF

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Warning: TT: undefined function: 32Steel design toAS 4100Flexural membersUniversity of South Australia受弯构件Flexural Member - DefinitionAny member that carries loads via flexing orbending受弯构件-定义任何通过弯曲或弯曲承载荷载的构件◼ member that has a bending moment 有弯矩的构件M*x  min ( Msx ;  Mbx)M*y   MsyClause 5.Streng...

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Steel design to AS 4100 Flexural members University of South Australia

受弯构件

受弯构件-定义

Flexural Membe Any member that carries loads via bending 任何通过弯曲或弯曲承载荷载的构件

◼

member that has a bending moment 有弯矩的构件

正常使用极限状态

Serviceability limit state AS 4100 Appendix B provides limited guidance AS 1170.0 Appendix C gives detailed guidance Load combinations in AS 1170.0 (ignore long term effects for steel) Usual to consider AS 4100附录B提供了有限的指导

AS 1170.0附录C给出了详细的指导

AS 1170.0中的荷载组合（忽略钢的长期效应）

通常考虑

◼ ◼ ◼

G (↓) G + sQ (↓) Ws (↑)

强度极限状态为AS 4100

Strength limit state to AS 4100 受弯构件

Section 5 – Members subject to bending M*x  min ( Msx ;  Mbx) M*y   Msy

Clause 5.1

强度极限状态为AS 4100

Strength limit state to AS 4100 可能的故障模式：

Possible failure modes: yielding of section (Cl 5.2) local buckling (Cl 5.2) of

混凝土拱腹裂缝

截面屈服

 

flange web

局部屈曲（第5.2条） 轮缘 网状物

lateral / lateral torsional buckling (Cl 5.3 to 5.6) 侧向/侧向扭转屈曲

上翼缘局部屈曲

Strength limit state to AS 4100 钢受弯构件的一般临界荷载组合：

Usual critical load combinations for steel flexural members: ◼ ◼

1.2G + 1.5Q 0.9G + Wu (roof)

截面弯矩承载力，第5.2.1条

Section moment capacity, Cl 5.2.1 Plate element

标称截面承载力

Nominal section capacity Ms = fy Ze Function of cros geometry and yield strength Consider any beam cross-section as a group of flat plate elements Each element in compression may be subject to local buckling before section yield

截面几何与屈服强度的函数

将任意梁截面视为一组平板单元

受压构件在截面屈服前可能会发生局部屈曲

Failure modes

失效模式

Plastic hinge 塑料铰链

Elastic 弹性的 Stresses less than yield 小于屈服的应力

Partially plastic 部分塑性 Stresses partially at yield

 y

y

Fully plastic 全塑性 Stresses fully at yield

部分屈服应力

y

NA

y

y

y Stress distribution at mid span

Bending failure

跨中应力分布 弯曲破坏

屈服应力

Failure modes

Local flange buckling 局部法兰屈曲

截面弯矩承载力

Section Moment capacity Determine whether local buckling will reduce section capacity Possibilities: 确定局部屈曲是否会降低截面承载力

可能性：

◼





Compac plastic capacity attained before local buckling (Cl 5.2.3) 紧凑-局部屈曲前达到的塑性承载力（第5.2.3条） 非压实-局部屈曲前屈服，但不能达到全塑性承载力（第5.2.4条） Non-compact - yield before local buckling but can’t attain full plastic capacity (Cl 5.2.4) Slender - local buckling occurs before yield (Cl 5.2.5) 屈服前发生细长局部屈曲

Section Moment Capacity 截面弯矩承载力

M Mp compact

紧凑

My non compact slender 细长的

非紧凑型



Member capacity 取决于梁在达到截面承载力之前是否会横向屈曲

Depends on whether beam will buckle laterally before reaching section capacity Lateral Torsional Buckling 3.31min Explanation Load Test showing LTB 4.15min Load Test – no lateral restraint 1.37min Load Test – include lateral restraint 2.09min

Function of  

span length 跨距 position, type and spacing of lateral and torsional restraints at the ends and along the beam 端部和梁沿线横向和扭转约束的位置、类型和间距

Flexural – torsional buckling

Flexural-torsional buckling (from The Behaviour and Design of Steel Structures to AS 4100, 3rd ed, Trahair & Bradford, Fig. 6.1) 弯扭屈曲（从钢结构的性能和设计到AS 4100，第3版，Trahair&Bradford，图6.1）

Class Activity Group #1 What is a fly brace ? 飞行支架 Where is it used and what does it do ? Group #2 What is a shear stud ? 剪力钉 Where is it used and what does it do ? Group #3

全高加强筋

What is a full height stiffener ? Where is it used and what does it do ?

Class Activity Group #4 预拱度 What is a Pre-cambering ? Where is it used and what does it do ? Group #5 预设 What is a Pre-Setting ? Where is it used and what does it do ? Group #6 预弯曲 What is a Pre-deflecting a beam? Where is it used and how does it work ?

Lateral restraint

横向约束

如果梁完全受到横向约束，构件承载力=截面承载力，计算结束

If a beam is fully laterally restrained, member capacity = section capacity, end of calculation Examples: 上翼缘现浇混凝土楼板和上翼缘栓钉的钢梁 固定在顶部或侧面的带紧密托梁的钢制地板支撑 



steel beam with cast in-situ concrete floor on top flange and top flange studs into concrete steel floor bearer with closely spaced joists fixed to top or fixed to side

If unsure, Cl 5.3.2.4 applies for standard sections

Segment length 约束之间的长度不是梁的长度

（除非没有中间限制）

Length between restraints is NOT the beam length (unless there is no intermediate restraints) Example: Rafter with simply supported span of 8m, and purlins at 1200 cts on top flange 简支跨度为8米的椽子，顶部翼缘为1200 cts的檩条  1.2G + 1.5Q (top flange compression) 上翼缘板压缩 Lez = 1200 mm 下翼缘板压缩  0.9G + Wu (bottom flange compression) Lez = 8000 mm (or between fly-braces if present) 在飞撑之间

Members not fully lateral restrained Cl 5.6 构件标称承载力 Nominal member capacity Mb = msMs  Ms m= moment modification factor 力矩修正系数 For constant BM, m= 1. This is a conservative value that can be used in all cases except cantilevers. m= 1 for all design capacity tables (DCT) otherwise use Table 5.6.1, remember this is for beam segments and ß m may not be the same as in Cl. 5.3.2.4 对于恒定BM，αm=1。这是一个保守值，可以用于除悬臂以外的所有情况。所有设计容量表 （DCT）的m=1. 否则，请使用表5.6.1，记住这是针对梁段的，且ßm可能与第5.3.2.4条中的不同

长细比折减系数

 s slenderness reduction factor 取决于Mo=参考屈曲力矩Mo取决于梁段的有效长度

Depends on Mo = reference buckling moment Mo depends on effective length of beam segment effective length le = ktklkrl  kt = twist restraint, usually = 1 扭转约束  kl = load height, important for top flange loads between restraints, and cantilevers 荷载高度，对约束装置和悬臂之间的上翼缘荷载很重要 

kr = rotation restraint, usually = 1 旋转限制

Example B2 A simply supported universal beam spanning 8m carries a central point load, due to storage live load of P = 100kN. Assuming the beam to be fully restrained at supports and laterally restrained at the load point determine a suitable section (Grade 300 PLUS). Allowable deflection = span/250. Neglect beam self weight. 由于储存活荷载P=100kN，跨度为8m的简支通用梁承受中心点荷载。 假设梁在支座处受到完全约束，并在荷载点处受到横向约束，确定合适的截面（300级以上）。 允许挠度=跨度/250。 忽略梁自重。

Example B2 (cont.) Lateral restraint

Segment AB lez = 4000mm

Segment BC lez = 4000mm

Span, L = 8000mm

Segment AB BM shape

Ex. B2 - serviceability Ps = s * P = 1.0 * 100 = 100kN Max deflection = Ix  Choose a 410 UB 53.7 kg/m section, Ix = 188 * 106 mm4 Onesteel Table 13

Ex. B2 - section capacity

Pu = 100 * 1.5 = 150 kN M* = PL/4 = (150 * 8)/4 = 300 kNm M*   Msx =  fyZex = 0.9 * 320 * 1060 = 305 kNm > M* (Use the fy value for the flange for bending checks as the flange carries most of the bending moment) - Since the 410UB53.7 is only just adequate for section capacity, it is unlikely to be adequate for member capacity. - Choose a 410 UB 59.7 (Zex = 1.2 * 106 mm3) Onesteel Table 14 （使用翼缘板的fy值进行弯曲检查，因为翼缘板承载大部分弯矩） -由于410UB53.7仅适用于截面承载力，因此不太可能适用于构件承载力。

Ex. B2 - effective lengths 梁包含两个节段，每个节段长4米

The beam contains two segments between the restraints each 4m long, each FL Twist restraint factor kt = 1.0 扭转约束系数 Load height factor k l = 1.0 (segment end) Lateral rotation restraint factor k r = 1.0 侧向旋转约束系数 Effective segment length, Lez = kt kl kr L= 4m (= 4000mm)

横向约束

Ex. B2 - lateral restraints 完全侧向约束的节段，如果：

Segment fully laterally restrained if:

where ßm = 0/300 = 0, 弯曲翼缘板值 fy = 300 MPa (use flange value for bending) Actual Lez/ry = 4000mm/39.7mm = 100 > 73 Hence, beam is not fully laterally restrained 梁未完全受到横向约束

Ex. B2 - Member capacity Mbx = m s Msx  Msx m = 1.75 + 1.05 m + 0.3 m 2 = 1.75 Table 5.6.1 Moa =

Cl 5.6.1.1 p 59

= 355 * 106 Nmm where Iy = 12.1 * 106 mm4, Iw = 467 * 109 mm6 le = 4000 mm, J = 337 * 103 mm4 Onesteel Table 13

Ex. B2 - member capacity cont. Msx = fyZex = 300 * 1200 * 103 Nmm = 360 kNm = 0.596 Cl 5.6.1.1 p 59

m s = 1.75  0.596 = 1.04 >1  m s = 1 Mbx = m s Msx = 1  360 = 360 kNm

Mbx = 0.9 x 360 = 324 kNm > M* = 300 kNm Hence satisfactory

Key points 1 - bending - Serviceability or deflection may govern beam design and must be checked particularly for deflection sensitive elements ie lintels and floor beams carrying brittle loads. This also gives a beam size to check for strength. 可使用性或挠度可能决定梁的设计，必须特别检查挠度敏感元件，如过梁和承受脆性荷载的地板梁。 这也给出了检查强度的梁尺寸。 - Serviceability load combinations usually checked are: 通常检查的可用性荷载组合为：  G  G + sQ where s = 0.7 for all cases except storage whens = 1.0  Ws

Key points 2 - bending Strength limit state check includes Section capacity and Member capacity. Usual load combinations checked are: 强度极限状态检查包括截面承载力和构件承载力。检查的常用荷载组合为： ◼ ◼

1.2G + 1.5Q 0.9G + Wu

Section capacity is independent of beam span and restraints and depends on material and cross-section properties only 截面承载力与梁跨度和约束无关，仅取决于材料和截面特性 Member capacity will usually govern strength check 构件承载力通常决定强度校核

Key points 3 - bending - For determining design shears, bending moments and deflections, the full beam length or span is used in calculations. - For determining member capacity the segment length of the beam is used, i.e. the distance between points of restraint of the compression flange of the beam. - It may be necessary to check more than one beam segment to determine the critical value. - m can be assumed to be = 1 for all beams except for cantilevers. This is a conservative assumption and very conservative for point loads on beams though. -为了确定设计剪力、弯矩和挠度，计算中使用全梁长度或跨度。 -为了确定构件承载力，使用梁的节段长度，即梁的受压翼缘约束点之间的距离。 -可能需要检查多个梁段以确定临界值。 -αm可以假设为除悬臂梁外的所有梁的值=1。这是一个保守的假设，但对于梁上的点荷载来说非常保守。...