Mechanics 1H

# Mechanics 1H - F x = 0 R A x = 0 F y = 0 R A y − P = 0 R...

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2.001 - MECHANICS AND MATERIALS I Lecture #5 9/20/2006 Prof. Carol Livermore TOPIC: FORCES AND MOMENTS TRANSMITTED BY SLENDER MEM- BERS? When will a structure fail? Recall: 1. What can the structural elements tolerate? 2. What forces and moments are experienced in the various parts of the structure? EXAMPLE: Airplane EXAMPLE: Truss SLENDER MEMBERS Long, skinny structural elements 1

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L>>b ,L>>h EXAMPLE: Skis, Golf Clubs, I-Beams Local axes follow the beam. AXIAL FORCES: Forces that act along the axis of the slender member. FBD F ij ( x )= N ( x ) , i: face, j: direction, x: location SHEAR FORCES:
Summarize Internal Loads: Moments: M xz ( x 2 ) > 0x: face, z: axis, x 2 :loca t ion M xz ( x )= M z ( x ) Bending Moment Sign Convention

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N> 0 N< 0 V> 0 V< 0 M> 0 M< 0 4
± ± ± EXAMPLE: Calculating internal forces and moments Step 1: Find reactions at supports.

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Unformatted text preview: F x = 0 R A x = 0 F y = 0 R A y − P = 0 R A y = P M A = 0 M A − P a = 0 M A = P a 5 Step 2: If you have a multi-component structure, you will need to Fnd joint forces too. Step 3: ±ind internal forces and moments. 1. Set up local coordinates. 2. Identify interesting points. 3. Cut beam and do ±BDs. 6 ± ± ± ± ± ± For 0 < x < a F x = 0 N = 0 F y = 0 P − V y = 0 P = V y M A = 0 P a + M z − P x = 0 M z = P x − P a = − P ( a − x ) OR (From the other end) FBD F x = 0 − N = 0 N = 0 F y = 0 − P + V y = 0 V y = P M ∗ = 0 − M z − P ( a − x ) = 0 7 ± ± ± M z = − P ( a − x ) Note: This is the same as before. For a < x < L F x = 0 − N = 0 N = 0 F y = 0 V y = 0 M ∗ = 0 − M z = 0 M z = 0 Step 4: Plot result and sanity check. 8...
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Mechanics 1H - F x = 0 R A x = 0 F y = 0 R A y − P = 0 R...

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