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Unformatted text preview: Instructor: T.A. Morgan CE 130 University of California, Berkeley Mechanics of Materials I Spring 2008 Midterm #2 Name Scoring Instructions This exam is closed book. For reference, a formula sheet is attached. You must submit
this formula sheet along with your exam. Please write your name at the top of all sheets
submitted. Clearly state any assumptions you make beyond what is described in the
problem. You may assume small angle approximations are valid. Partial credit may be
awarded based on understanding of principles embedded in each problem. Therefore
extraneous or irrelevant computations will decrease your overall score where the ﬁnal
answer is incorrect. If you need more space to write, use the back of the page. The duration of the examination is 50 minutes. Good Luck 10f7 Name: _
Midterm #2 Problem 1 (20' points) Consider the column shown below, having height H and square cross section (with each
side having dimension 5.) A load P is applied at the top, but is offset from the centroid
of the section by an eccentricity e [as shown in the ﬁgure.) The material is brittle [like
chalk) and is very weak in tension. Ignore the self—weight of the column. All answers should be expressed in terms of parameters given. ABM E ‘ 3.) Write the ordinary differential equations (ODE‘s) describing u($) and 11(3), where u
is the axial displacement, and u is the transverse displacement. Include boundary conditions (BC‘s) for each. See the space provided below for your answer. Note: you
are only asked to write the ODE’s and 30’s, n_ot to solve them. b) What is the maximum eccentricity e such that no tension stress occurs anywhere in
the column? location of P  "tr
rw— to
H . if 4.9% 5*: C3 togview dx {
P—¢A= U
3 1—, 'Qam We : ‘3 325 its»: «as. i :.l I
For use in answering part a) ll '2. : Q
ODE for spy): '0 E M see for u(;z:): m f:
E— + .
ill—h lo Emil 'n I C)
ODE for v(.r): l7 “ P
BC‘sfoweywo) EWW“ €— s) 03f Name: [MWVBW
Midtcmn #2 Problem 2 (20 points) Consider the hanging cantilever beam with end load P, shown below. The beam is
composed of two rectangular beams nailed together with two rows of nails. Each nail has an allowable shear force F”. All answers should he expressed in terms of parameters given. a) Draw and shear diagram WI} and the moment diagram M for this beam and the
given loading. b) For each of the two spans indicated, what is the required nail spacing? You should have two answers one for S )an 1 and another for 3 Jan 2.
1 3 SD“ 1 Span 2
' ’ _.xk_ P_ JIM.“ in 40f? Name: anﬁ‘i’hu. '
Medium #2 (Problem 2, continued) 50f? Nulue: '
liftdtcrm #2 Problem 3 (10 points) (Ionsit'ler a beam with rectangular cross section” shown below (left) This beam is
composed of a material with nonlinear stress—strain relation given by the equation
(I 2 Us”? (shown below, right). The material response in compression and tension is
the same. Derive the expression for the beam moment M about the zuaxis in terms of the curvature. N. Your answer should be expressed in terms of parameters given. If tTl Beam section Material stress—strain relation use. Gel7 ...
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 Spring '07
 Hutchings

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