1032_L8

Information about 1032_L8

Published on July 26, 2014

Author: puja.pooo

Source: authorstream.com

Content

8/1 STRESS AND STRAIN IN BEAMS: 8/1 STRESS AND STRAIN IN BEAMS 8/2 BENDING BEAMS: 8/2 BENDING BEAMS LOADS ON BEAM PRODUCE STRESS RESULTANTS, V & M V & M PRODUCE NORMAL STRESSES AND STRAINS IN PURE BENDING V & M PRODUCE ADDITIONAL SHEAR STRESSES IN NON-UNIFORM BENDING 8/3 TYPES OF BENDING: 8/3 TYPES OF BENDING PURE BENDING – FLEXURE UNDER CONSTANT M. i.e. V =0 = dM/dx NON-UNIFORM BENDING – FLEXURE WHEN V NON-ZERO 8/4 PURE BENDING: 8/4 PURE BENDING P P Pure bending region x z y Unit (small) Length P -P M V P.a a Non –uniform bending 8/5 PURE BENDING: 8/5 PURE BENDING Unit (small) length Straight lines M M 8/6 RADIUS OF CURVATURE : 8/6 RADIUS OF CURVATURE  Straight lines remain straight Planes remain plane  8/7 CURVATURE  = 1/: 8/7 CURVATURE  = 1/   d  ds dx x y PowerPoint Presentation: d= dx L 1 = (  -y)d  L 1 = dx - (y/  )dx L 1 - dx = -(y/  )dx L 1  x = -(y/  )dx/dx=-  .y NORMAL STRAIN NEUTRAL AXIS 8/9 LONGITUDINAL STRAIN: 8/9 LONGITUDINAL STRAIN 1 y Strain  x 8/10 LONGITUDINAL STRESS: 8/10 LONGITUDINAL STRESS y Strain Stress   Stress v Strain 8/11 NORMAL STRESS AND STRAIN: 8/11 NORMAL STRESS AND STRAIN 1 y Strain Stress  x = -y/  = -  .y  x = E.  x  x = -E.y/  = -E.  .y  x 8/12 RELATION BETWEEN  & M: 8/12 RELATION BETWEEN  & M NEED TO KNOW WHERE NEUTRAL AXIS IS. FIND USING HORIZONTAL FORCE BALANCE NEED A RELATION BETWEEN  & M. FIND USING MOMENT BALANCE –gives THE MOMENT CURVATURE EQUATION & THE FLEXURE FORMULA 8/13 NEUTRAL AXIS PASSES THROUGH CENTROID: 8/13 NEUTRAL AXIS PASSES THROUGH CENTROID First moment of area  x M y x z dA y c 1 c 2 Compression Tension 8/14 MOMENT-CURVATURE EQN: 8/14 MOMENT-CURVATURE EQN z y c 1 c 2 dA = moment of inertia wrt neutral axis 8/15 FLEXURE FORMULA FOR BENDING STRESSES: 8/15 FLEXURE FORMULA FOR BENDING STRESSES 8/16 MAXIMUM STRESSES: 8/16 MAXIMUM STRESSES OCCUR AT THE TOP & BOTTOM FACES 8/17 MAXIMUM STRESSES: 8/17 MAXIMUM STRESSES S 1 = I/c 1 Section modulus  1 M y x  2 C 1 C 2 8/18 I & S FOR BEAM: 8/18 I & S FOR BEAM 0 h b z y 8/19 BEAM DESIGN: 8/19 BEAM DESIGN SELECT SHAPE AND SIZE SO THAT STRESS DOES NOT EXCEED  ALLOW CALCULATE REQUIRED S=M MAX /  ALLOW CHOOSE LOWEST CROSS SECTION WHICH SATISFIES S 8/20 IDEAL BEAM: 8/20 IDEAL BEAM RECTANGULAR BEAM, S R =bh 2 /6=Ah/6 CYLINDRICAL BEAM, S=0.85.S R IDEAL BEAM, HALF THE AREA AT h/2 IDEAL BEAM, S=3.S R STANDARD I-BEAM, S=2.S R 8/21 STRESSES CAUSED BY BENDING: 8/21 STRESSES CAUSED BY BENDING q=20kN/m P=50kN R A R B 2.5m 3.5m h=0.7m b=0.22m 8/22 V & M DIAGRAMS: 8/22 V & M DIAGRAMS V=89.2kN 39.2kN -10.8kN -80.8kN M=160.4kNm V M 8/23 MAX FOR BEAM: 8/23  MAX FOR BEAM 0 h b z y MAXIMUM STRESSES

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