Slide1: 1 Design of steel flexural members Prepared by C.MAKENDRAN M.E.,(Ph.D) Assistant Professor,
Slide2: 2 Real world steel beams
Slide3: 3 Prismatic members loaded along their axes Load is carried by tension and compression
Slide4: 4 Load is carried by moment + shear BM diagram SF diagram Concentrated load
Slide5: 5 Most bridge girders are simply supported
Slide6: 6 Beam under uniformly distributed load( moment + shear) BM diagram SF diagram
Slide7: 7 FIXED BEAM BM diagram SF diagram
Slide8: 8 Rectangular cross section Bending stresses Shear stresses Stresses in cross sections under bending Tension Compression
Slide9: 9 Rectangular cross section Bending stresses I sections under bending Tension Compression Shear stresses
Slide10: 10 Deep Beam or Timoshenko Beam Thin beam or Euler Bernoulli beam Flexure dominates Shear dominates
Slide11: LIMIT BEHAVIOUR OF LATERALLY RESTRAINED BEAMS AND ITS DESIGN
Slide12: Lateral-torsional buckling Flexural yielding TYPES OF BEAM BEHAVIOUR
Various modes of beam failure: Various modes of beam failure
Laterally supported beams: Laterally supported beams
Limit states for LR beams: Limit states for LR beams Limit state of flexure Limit state of shear Limit state of bearing Limit state of serviceability
Slide16: M Radius of curvature Curvature of bending (a) (b) A z M h c Deflected shape N A
Slide17: Stress 1 strain 2 3 4 f y Plastic range Elastic range Idealised elasto- plastic stress stain curve for the purpose of design Idealised stress strain curve f
Slide18: 1 < y 2 = y f 2 =f y f 1 <f y Strain and stress distributions in the elastic range 2 1
Slide19: 3 > y f 3 =f y f 3 <f y Strain and stress distributions in plastic range 4 >> y f 4 =f y 4 A C A T Z c Z T B 3 f y T d t d 0 d 0 z c z T Stress Strain Strain Stress
Slide20: 1 2 4 3 f y f y f y (b) Plastification of cross section <f y M y M P M (a) BM diagram 2 1 4 2 1 (c) Curvature Diagram Curvature max at collapse 3 4 3
Slide21: 1 2 3 4 Plastic Hinge Simply supported beam and its deflection at various stages
Slide22: 2 1 3 4 Design strength of different class of beams
Slide23: 2.0 1.7 1.27 1.14 1.5 Some typical shape factor
Slide24: Flexural Capacities of LR beams
Slide25: 25 FIXED BEAM BM diagram SF diagram
Slide26: 26 Rectangular cross section Bending stresses I sections under bending Tension Compression Shear stresses
Slide27: 27 FIXED BEAM – External BM SF diagram BM diagram 27 Internal moment and shear resistance
Slide28: Stress 1 strain 2 3 4 f y Plastic range Elastic range Idealised elasto- plastic stress stain curve for the purpose of design Idealised stress strain curve f
Slide29: 2 = y f 2 =f y Strain and stress distributions in the elastic range 2
Slide30: 30 Rectangular cross section Bending stresses I sections under bending Stage II Tension Compression Shear stresses My
Slide31: 3 > y f 3 =f y f 3 <f y Strain and stress distributions in plastic range B 3 f y T d t d 0 d 0 z c z T Stress Strain
Slide32: 32 Rectangular cross section Bending stresses I sections under bending stage III Tension Compression Shear stresses >My <Mp
Slide33: Strain and stress distributions in plastic range 4 >> y f 4 =f y 4 A C A T Z c Z T Strain Stress
Slide34: 34 Rectangular cross section Bending stresses I sections under bending Stage IV Tension Compression Shear stresses Mp
Slide35: 35 Rectangular cross section Bending stresses Stress distribution for low shear problems Tension Compression Shear stresses Mp
Slide36: 36 Rectangular cross section Bending stresses Stress distribution for high shear problems Tension Compression Shear stresses <Mp
Slide37: IS:800 Draft-22.04.04 37 8.2 Design Strength in Bending (Flexure) The factored design moment, M at any section, in a beam due to external actions shall satisfy 8.2.1 Laterally Supported Beam The design bending strength as governed by plastic strength, M d , shall be taken as M d = b Z p f y / m0 1.2 Z e f y / m0 PROVIDED THE SHEAR IS LOW OTHERWIDE REDUCE Md
Combined Shear and Bending: Combined Shear and Bending a) Plastic or Compact Section b) Semi-compact Section
Slide39: Other Limit States of beams
Slide40: Combined bending and shear in beams Elastic Bending stress Elastic Shear stress Plastic range a b c LIMIT STATE OF SHEAR
Slide41: 41 EQUATIONS FOR PLASTIC SHEAR CAPACITY
Slide42: 42 BUCKLING OF WEBS
Slide43: 43 Shear Buckling of web
Slide44: Shear buckling of a plate BUCKLING OF WEB PLATES IN SHEAR cr
Slide45: 45 8.4 Shear The factored design shear force, V , in a beam due to external actions shall satisfy V V d V d = design strength calculated as , V d = V n / γ m0 8.4.1 The nominal plastic shear resistance under pure shear is given by: V n = V p A v = shear area Cont…
Slide46: 46 45 0 d / 2 d / 2 b 1 n 1 Effective width for web buckling LIMIT STATE OF WEB BUCKLING
Slide47: 47 b 1 n 2 1:2.5 slope Root radius Effective width of web bearing Web Crippling in beams LIMIT STATE OF WEB CRIPPLING
Slide48: Thank You