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# 10.01.03.034

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### Transcript of "10.01.03.034 "

1. 1. Powerpoint Templates
2. 2. PRESENTATION ON • Bullet point • Bullet point
3. 3. STRESS The components of the intensity of force per unit area- that is stress.
4. 4. 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.
5. 5. 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)
6. 6. 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)
7. 7. 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
8. 8. 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.
9. 9. Uniaxial Bending Stress (Cont.) Bending stress is distributed through a beam as seen in the diagram below:
10. 10. 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.
11. 11. Uniaxial Bending Stress (Cont.) EXAMPLES: A beam under only a bending load will be in a uniaxial. Stress (force) distribution in a bent beam
12. 12. 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.
13. 13. 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.
14. 14. 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.
15. 15. Biaxial Bending Stress (Unsymmetric Bending)  A biaxial stress system has a stress state in two direction. . It is also known as unsymmetrical (skew) bending.
16. 16. Biaxial bending stress (Unsymmetric Bending) The formula of the biaxial bending stress is given by- σx = -(Mz Y/Iz ) + (MyZ/Iy)
17. 17. 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.
18. 18. 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
19. 19. Thank You………..
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