Lec1
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This document provides an overview of the 2.001 Mechanics and Materials I course, which covers statics, displacements and deformations, and constitutive laws. It outlines the plan for the first lecture, including reviewing vectors, forces, moments, and equilibrium. It also provides instructions on how to solve problems using good sketches, symbolic solutions, and checking answers. Key concepts introduced are that forces and moments are vectors, and the equations of static equilibrium that must be satisfied.
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Lec1
- 1. 2.001 - MECHANICS AND MATERIALS I Lecture #1 9/6/2006 Prof. Carol Livermore A 鍖rst course in mechanics for understanding and designing complicated systems. PLAN FOR THE DAY: 1. Syllabus 2. Review vectors, forces, and moments 3. Equilibrium 4. Recitation sections BASIC INGREDIENTS OF 2.001 1. Forces, Moments, and Equilibrium Statics (No acceleration) 2. Displacements, Deformations, Compatibility (How displacements 鍖t to- gether) 3. Constitutive Laws: Relationships between forces and deformations Use 2.001 to predict this problem. HOW TO SOLVE A PROBLEM RULES: 1. SI inits only. 2. Good sketches. Labeled coordinate system.
- 2. Labeled dimensions and forces. 3. Show your thought process. 4. Follow all conventions. 5. Solve everything symbolically until the end. 6. Check answer Does it make sense? Check trends. Check units. 7. Convert to SI, plug in to get answers. VECTORS, FORCES, AND MOMENTS Forces are vectors (Magnitude and Direction) i j F = Fx + Fy + Fz k OR F = Fx i + Fy j + Fz k Where do forces come from? Contact with another object Gravity Attractive of repulsive forces Moments are vectors. (Moment is another word for torque.) Forces at a distance from a point Couple
- 3. Moments are vectors. M = My j. EX: 2D: FB = FBx + FBy i j rAB = rABx + rABy i j MA = rAB FB = = (rABx + rABy (FBx + FBy i j) i j) = (rAB FB rAB FB )k x y y x OR MA = |rAB | FB sin using Right Hand Rule 3D: i j rAB = rABx + rABy + rABz k i j FB = FBx + FBy + FBz k MA = rAB FB = (rABx FBy rABy FBx )k +(rABz FBx rABx FBz ) j+(rABy FBz rABz FBy ) i 3
- 4. EX: Wrench rAB = d j FB = FB i j i MA = rAB FB = d FB = dFB k Equations of Static Equilibrium 裡Fx = 0 裡F = 0 裡Fy = 0 裡Fz = 0 裡M0 x = 0 裡M0 = 0 裡M0 y = 0 裡M0 z = 0
- 5. 4 F =0 i=1 F1 + F2 + F3 + F4 = 0 F1x + F2x + F3x + F4x = 0 F1y + F2y + F3y + F4y = 0 F1z + F2z + F3z + F4z = 0 Mo = 0 r01 F1 + r02 F2 + r03 F3 + r04 F4 = 0 i, j, a. Expand in k . b. Group. c. Get 3 equations (x,y,z). Try a new point? Try A. rA1 = rA0 + r01 ... MA = 0 rA1 F1 + rA2 F2 + rA3 F3 + rA4 F4 = 0 (rA0 + r01 ) F1 + (rA0 + r02 ) F2 + (rA0 + r03 ) F3 + (rA0 + r04 ) F4 = 0 rA0 (F1 + F2 + F3 + F4 ) + (r0 1 F1 + r0 2 F2 + r0 3 F3 + r0 4 F4 ) = 0 rA0 (F1 + F2 + F3 + F4 ) = 0 F =0 (r0 1 F1 + r0 2 F2 + r0 3 F3 + r0 4 F4 ) = 0 M0 = 0 So taking moment about a new point gives no additional info. 5