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Unformatted text preview: 9:00  10: 00 NAME February 27, 2004 MNHFUEE) @MDZ ﬁll/11$ (Beam Handout, (equations of elasticity handout available on request) no
books, no notes; calculators allowed) Put your name on the top page, and on each subsequent page of the exam if you disassemble the pages. Read all questions carefully. Do all work on that question on that page. Use back of that page if necessary. Show all your work, especially intermediate results. Partial credit cannot be given
without intermediate results. Show the logical path of your work. Explain clearly your reasoning and what you are
doing. In some cases, the reasoning is worth as much (or more) than the actual answers.
Be sure to show the units as well (if necessary). Final answers are not correct without the units. State any assumptions you are making
Report significant digits only.
Box your final answers. EXAM SCORING
#1 (24%) #2 (25%)
#3 (26%)
#4 (25%) FINAL SCORE Unified Quiz 1MS
February 27, 2004 NAME PROBLEM #1 (24%) The questions that follow should require only a few sentences as answers, or
very simple calculations. Provide sufficient detail to support your answer, but
be brief. a.) Structural steel girders and aluminum wing spars are often made with an "I"
cross section rather than a solid rectangular crosssection, Why is this? Tm. 014W «wk OWQW dl' 0* MGM" “We
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b Estimate the maximum tensile stress in the structure below, loaded by a load
of 100 kN. 0 Aircraft structures are designed according to requirements of high strength and
stiffness and low mass. Steel, aluminum and titanium alloys all have virtually identical
stiffness to density ratios (E/p) and strength to density ratios (O/p). And yet aluminum is the material predominantly used for commercial transport airframes.
Why? Unified Quiz 1MS
February 27, 2004 NAME PW ww “ML omﬂw M Wags, taste a:
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chill wl tux (runtht/LD. m Q) Pd . (:1 Simple beam theory is derived based on the assumption “plane sections remain
planar and perpendicular to the midplane of the beam” This only strictly applies to beams
under pure bending (i.e with no shear forces). In general beams will carry shear forces.
Justify the applicability of simple beam theory to cases where shear forces are present. Skew oat/me» Cawci OW Mums) 0W1 0km
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February 27, 2004 NAME PROBLEM #2 (25%) A uniform bar of length 2L and cross sectional area A (with a solid circular cross—
section), made of a material of density p, Young's modulus E and yield stress, 0y, rotates at constant angular velocity (u about an axis through its center, perpendicular to its length (see figure below). You should assume that no transverse forces or
moments or torques act on the bar. \NE a a) Determine and sketch F(x), the internal axial force distribution along the bar. Hint. The centrifugal force, F, required to keep a point mass m rotating in a circle radius r at a
speed so is F=mroo2 Cam/NM ‘e/er
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(F‘CDQA b) Calculate the extension of the bar. 3mm; Z : (Sire xx __.._/ Unified Quiz 1M8
February 27, 2004 NAM E PROBLEM #3 (26%)
A simply supported beam is loaded by a point load P, 1/3 of the way along its length as
shown below: P
A B
C
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L/3 2L/3 a) Calculate and sketch the bending moment and shear force distributions as a function of
position along the beam. Note the maximum values of each and their locations. Unified Quiz 1MS
February 27, 2004 NAME b) The beam has a rectangular crosssection, height h, breadth b. It is made of a material
with a Young’s modulus E and a yield stress, 0y. Outline the process you would use to calculate the deflection of point C, the loading point. Write down all relevant
equations and quantities where known, but do not solve the resulting equations. 1‘4 MM? J]? Mk I: 5‘“? Unified Quiz 1MS
February 27, 2004 NAME PROBLEM #4 (25%) A beam of length L and flexural rigidity El is clamped at each end. The beam has a point load
of magnitude P applied at the mid point of the beam. P \\\\&< >
th\\\‘ 1 B
c L/2 _/2 Outline a solution approach to calculate the deflection of point C of the midpoint of the
beam. Write down the relevant (final) equations you will need to use, describe
how you would use them, but do not solve them. TIM lb 0» Ola—JCT Lialie) [WCL‘QJ’CA/V‘Ukkvlﬂ CMLA MC OWWQSJ‘LM, Miami ire emcLAQF l’b “Jul/b; OLMWKMMM CM (J), (5W
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 Fall '05
 MarkDrela
 Force, Shear Stress, Shear forces, simple beam theory

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