Assing 1M - 2 The moment of inertia of the beam is I all the way along its length You are welcome to use the table in Appendix C whenever it would

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.001 Mechanics and Materials I Fall 2006 Problem Set 11 Distributed: Wednesday, November 29, 2006 Due: Wednesday, December 6, 2006 Problem 1: Hibbeler 12-15 Problem 2: Calculate the deflection v(x) of the beam below by direct integration. What is the deflection of the beam at point A? The beam has a uniform Young’s modulus of E, and the moment of inertia of the cross section is I. w B C A x L L Problem 3: Calculate the deflection and slope at the center of the beam below using superposition and the results in Appendix C. L/2 A B P C L/2 P x Problem 4: Using superposition, calculate the deflection in the center (point B) of the beam shown below. The beam has a moment of inertia I and a Young’s modulus E. P A x B C L/2 L/2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Problem 5: Calculate the deflection at the tip of the cantilever below. The half near the support has a Young’s modulus of E 1 , and the half away from the support has a Young’s modulus of E
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2 . The moment of inertia of the beam is I all the way along its length. You are welcome to use the table in Appendix C whenever it would be useful. A B C M E 1 E 2 L/2 L/2 Problem 6: Consider the composite beam cross section shown below. The top part of the beam (shaded) has a Young’s modulus of E 1 , and the bottom part of the beam (hatched) has a Young’s modulus of E 2 = 2E 1 . The directions of y and z are marked; it’s up to you to decide where to locate the origin. First locate the neutral axis in the beam. You will now examine the values of stress and strain on the dotted line indicated in the figure. Calculate the strain ε xx and the stress σ xx (as a function of the distance y off the neutral axis) that would result from an applied moment M about the z axis. Then graph both ε xx and σ xx vs. y. b/2 b b/4 b/4 Direction of y a a Direction of z a...
View Full Document

This note was uploaded on 08/16/2009 for the course ENG C taught by Professor Prof during the Spring '09 term at Ohio University- Athens.

Page1 / 2

Assing 1M - 2 The moment of inertia of the beam is I all the way along its length You are welcome to use the table in Appendix C whenever it would

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online