10.01.03.034
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10.01.03.034

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10.01.03.034 10.01.03.034 Presentation Transcript

  • Powerpoint Templates
  • PRESENTATION ON • Bullet point • Bullet point
  • STRESS The components of the intensity of force per unit area- that is stress.
  • Bending Moment Stress If the stress in a beam depends on the bending moment is called bending moment stress. It is the internal stresses caused by bending moments acting at a given distance from the neutral axis. It is also known as flexural stress.
  • Bending Moment Stress (Cont.) The formula for bending stress, σ, is as follows: σ = My/ I  M = moment acting on beam from moment diagram (kip-in or lb-in)  y = distance from neutral axis to extreme edge of member (in)  I = moment of inertia about the axis (in^4)
  • Bending Moment Stress (Cont.)  Recalling that S = I/Y , the bending stress formula could be re-written as: σ = M/S where: S = section modulus about the axis (in³)
  • Types of bending moment stress Background Text & Lines Shadows Accent Accent & Hyperlink Title Text TWO TYPES OF BENDING STRESS  Fills Followed Hyperlink UNIAXIAL BENDING STRESS BIAXIAL BENDING STRESS
  • Uniaxial Bending Stress • An uniaxial bending stress system has a stress state in one direction. • In Diagram 1 we have shown a simply supported beam loaded at the center. It deflects (or bends) under the load.
  • Uniaxial Bending Stress (Cont.) Bending stress is distributed through a beam as seen in the diagram below:
  • Uniaxial Bending Stress (Cont.) EXAMPLES: A simply-supported beam always has tensile stresses at the bottom of the beam and compressive stresses at the top of the beam.
  • Uniaxial Bending Stress (Cont.) EXAMPLES: A beam under only a bending load will be in a uniaxial. Stress (force) distribution in a bent beam
  • Uniaxial Bending Stress (Cont.) Example GIVEN: A nominal 2x10 (actual dims. 1½” x 9¼”) is used as a simply-supported beam with loading as shown. The allowable bending stress is 1200 psi. REQUIRED: a) Determine the maximum moment on the beam. b) Determine the maximum actual bending stress on the beam c) Determine if the beam is acceptable based upon allowable bending stress.
  • Uniaxial Bending Stress (Cont.) The maximum bending moment, Mmax, on a simply-supported, uniformly loaded beam is: Mmax = wL2/8 or, Mmax = (140 PLF)(11') 2/8 or, Mmax = 2117.5 lb-ft The bending stress is: σ =M/S =[2117.5 lb - ft(12"/ft)] / 21.39 in³ or, σ = 1187.9 PSI Since the actual bending stress of 1187.9 PSI is less than the allowable bending stress of 1200 PSI, THE BEAM IS ACCEPTABLE.
  • Variation of tension and compression due to bending moment: With the shown sign convention, bending about X-axis causes compression in the top part and tension in the bottom region, whereas bending about Y-axis causes compression in the left hand part and tension in the right part. In biaxial bending (d), the top-left part is subjected to double compression and the bottom right part is subjected to double tension. The remaining parts are subjected to combined compression and tension.
  • Biaxial Bending Stress (Unsymmetric Bending)  A biaxial stress system has a stress state in two direction. . It is also known as unsymmetrical (skew) bending.
  • Biaxial bending stress (Unsymmetric Bending) The formula of the biaxial bending stress is given by- σx = -(Mz Y/Iz ) + (MyZ/Iy)
  • Biaxial bending stress (Cont.) EXAMPLES: The column having axial load acting in such a way that the load is eccentric about both the axes in the plane of the column then it is called biaxially loaded column.
  • Biaxial bending stress (Cont.) EXAMPLES: Schematic stress distribution of a rectangular footing under the effect of biaxial bending together with vertical load is shown in Figure: Loading at footing base and stress distribution
  • Thank You………..