FinalSolutionsWinter05

Structural Analysis (6th Edition)

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Unformatted text preview: Question Score 1 W2 W UNIVERSITY OF MICHIGAN +——~—~ Official Examination Booklet ___.7___.._,..___._ 8 Total Name of Student: ‘ Date of Examination: April 25, 2005 Course: CEE212 — Solid and Structural Mechanics NOTE: PLEASE HAND IN YOUR FORMULA SHEET WITH THE EXAM The University of Michigan Honor Code The Honor Code outlines standards for ethical conduct for graduate and undergraduate students, faculty members, and administrators of the College of Engineering at the University of Michigan. Policies 1 ‘1 When Taking Exam The instructor need not monitor the exam The instructor will announce the time of the exam and the instructor's whereabouts will be communicated to the class Students will allow at least one empty seat between themselves and their neighbor The instructor will inform the class prior to the exam if aids are allowed during the exam Students must write and sign the Honor Pledge on their exams The Honor Pledge is: I acknowledge that I have neither given nor received aid on this examination nor have I concealed any violation of the Honor Code. (Signed) QUESTION #1 (20 POlNTS) —~ Design of Columns for a New Campus Building The University of Michigan has hired your design firm to design a new Civil and Environmental Building on the North Campus. You decide to design the new building using steel (E = 29 x 106‘ psi) as the primary building material. Your design has an interesting column as shown: /—“ W10X39 t P i T‘ FM 3 ‘ ' ‘ y i 15feet l: . 1P A=‘11.5m2 rx=4.27in 10feet Ty: in y Elevation View Your analysis for the structural design tells you that each floor has a resultant load, P, applied to the column (as shown). The connection of the column to the foundation is done through a pin connection (as shown). Furthermore, the floor beams (2 are shown for each floor in the diagram above) do not restrain rotation at the connection. What is the maximum load this column can take (ignore the out~of—plane bucklinggase)? Afinfl an!» iv X 5§§3§va "23??" iv» gE f”; ,ia 3 4%53 €352 flying , V 7 7 gm” m... QUESTION #2 (2O POlNTS) —— Cantilevered Beam Deflections You are given the following cantilevered beam with the loading shown: 50 kN 50 kN A _ El 2 10 l\lll~l«l"n2 B l 1.5 m f 1.5 m 90 km" 1) Draw the moment diagram of the beam 2) Draw a rough deflected shape of the beam under the applied loading 3) Determine the rotation of the beam end at tip “B” 4) Determine the deflection of the beam end at tip “B” zéi§!ilt:li§5 .535: 3: Q6. QUESTION #3 (25 POlNT‘S) - Analyzing Shear Walls under Earthquakes Concrete structures located in zones of high seismic activity (such as California) are often subjected to earthquakes which act laterally on the structure. One structural system used to resist the earthquake’s lateral forces is the shear wall. Shear walls are made of concrete and are very strong at resisting the earthquake loading. However, concrete is weak in tension so the design of the shear walls must consider the weak tensile strength of concrete in their design. The following shear wall is shown below: ‘ Total Base Shear, V W \ Concrete Shear W all ' {Ftoor 1) l W20 teet~————~ 4 t:::::: ‘T 0.5 feet You are interested in analyzing the first floor portion of the shear wall. You identify two types of loadings on the wall: weight of the wall from above. W = 800 kips, and the shear load, Twig, distributed (average) over the cross section of the wall. The average shear stress, “CM, is due to the shear at the base of the shear wall, V = Atavg. The concrete is infinitely strong in compression and shear but will fail if the tensile stress exceeds 100 psi. When the tensile load on the concrete is 100 psi, the concrete will crack perpendicular to the direction of the tensile load. 1) Find the maximum shear load, V, the wall can take before it fails in cracking 2) Determine the angle of the cracks that form gggéfiggx KrHMMWrrymmMMwwww " ' QUESTION #4 (25 POINTS) — Design of an Overhanging Awning You are given the following cross section for a beam: 4 in.—-«——-——->i “rt WNW—Ma;— l. I Sc l l l I, ~w0~m~MMSinr w? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ »» l l l l 1) Determine the location of the shear center (SC) 2) Determine the distribution of shear stresses along the thin walled section if a 2.5 kip vertical shear, V, is applied at the shear center (SC). As part of your answer, please draw a diagram of the distribution with numbers added to your figure to show the shear stress at key locations along the section. 6:; : ,z’? :6: g ‘2? 537E335? 2\ .U Z '3»: a @3sz f TVwM~ r3 QUESTION #5 ( i O POlNTS) ~ General Questions 1) What is the general procedure for analysis when you have a statically indeterminate beam? (2 pt) 2) Given a distributed load, w{x), on a beam, how is the load related to the displacement of the beama v? (2 pt) 3) Define principal stresses: (2 pt) 4) Your first job as a structural engineer is to design a residential house for an affluent client in the Ann Arbor area. You choose timber as the material of construction of the house. After the structure is built and has been in service for a number of years, the owner calls you back to look at a few of the joists supporting the ceiling. You observe the beams are “splitting”; in other words, they are developing cracks parallel to the longitudinal axis of the beams (see Figure on next page). The cracks are forming from the two ends of the joist (both sides). It should also be noted that the grain of the wood runs parallel with the longitudinal axis of the beam. What is the owner witnessing - what type of failure is this? (4 pts.) Loading from the Roof “T W Cracking of Joist N Cracking of Joist ...
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This homework help was uploaded on 02/01/2008 for the course CEE 212 taught by Professor Lynch during the Winter '06 term at University of Michigan.

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FinalSolutionsWinter05 - Question Score 1 W2 W UNIVERSITY...

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