2.001 - MECHANICS AND MATERIALS I Lecture #2 9/11/2006 Prof. Carol Livermore TOPIC: LOADING AND SUPPORT CONDITIONS STRUCTURAL ANALYSIS Tools we need: 1. Recall loading conditions (last time)
a. Forces - ("Point Loads ") Magnitude Direction
Point of Applic
2.001 - MECHANICS AND MATERIALS I Lecture #3 9/13/2006 Prof. Carol Livermore Recall from last time:
FBD:
Solve equations of motion. Fx = 0 Fy = 0 MA = 0 See 9/11/06 Notes. Solution:
1
Draw each component separately. FBD of Bar 1
Fx = 0 FAx + FCx = 0 Fy =
2.001 - MECHANICS AND MATERIALS I Lecture #17 11/8/2006 Prof. Carol Livermore Recall: Stress Transformations
[ ] =
xx xy
xy yy
.
xz = yz = zz = 0
[ ] = x x = y y =
x x x y
x y y y
.
xx + yy xx + yy + cos 2 + xy sin 2 2 2 xx + yy xx - yy - cos 2 - xy sin 2
2.001 - MECHANICS AND MATERIALS I Lecture #20 11/20/2006 Prof. Carol Livermore Beam Bending Consider a "slender" (long and thin) beam
Q: What happens inside when we bend it? Assume: Cross-section and material properties are constant along the length Symme
2.001 - MECHANICS AND MATERIALS I Lecture #21 11/21/2006 Prof. Carol Livermore Recall from last time: Beam Bending
y = 0 on neutral axis -y xx = (Note: purely geometric, no material properties) xx = xx E (All other are equal to 0) So: xx = -Ey
Force Equi
2.001 - MECHANICS AND MATERIALS I Lecture # 22 11/27/2006 Prof. Carol Livermore Beam in pure bending = radius of curvature -y -Ey xx = xx = Locating the neutral axis Ey dA = 0 A Moment-Curvature 2 M = A Ey dA Special Case: E = constant Neutral Axis: ydA =
2.001 - MECHANICS AND MATERIALS I Lecture #23 11/29/2006 Prof. Carol Livermore Recall Moment-Curvature Equation E(x)I(x) or EIef f for composite beams. (x) 1 2v M (x) = = E(x)I(x) (x) x2 Approach: Integrate, get v(x), (x) = constants of integration. Libra
2.001 - MECHANICS AND MATERIALS I Lecture #26 12/11/2006 Prof. Carol Livermore Energy Methods 3 Basic Ingredients of Mechanics: 1. Equilibrium 2. Constitutive Relations - . . . Stress-Strain F - Force-Deformation 3. Compatibility Dealing with geometric co
2.001 - MECHANICS AND MATERIALS I Lecture # 27 12/13/2006 Prof. Carol Livermore Example Problems
Q: What is the force in the spring? FBD
4 unknowns 3 equilibrium equations statically indeterminate. Force-Deformation
F = k d v(x) M (x) = dx2 EI Compatibili