CE 470: Final Exam (11 December 2010) –Structural Steel Design(page 1/4)

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Department of Civil & Geological EngineeringUniversity of Saskatchewan

CE470.3 FINAL EXAMINATIONSaturday 9:00am, 11 December 2010, Room 2E25 AGRI Building

Time Allowed = 3 hours Instructor: M.M. Hrabok

Student Name: Number:

Notes: How many booklets and other sheets handed in: ______________• this is a “closed book examination” except the Student is allowed to bring in the CSA-S16-09 CISC

Handbook of Steel Construction (10th Edition) but not the Class Notes. Calculators are permittedbut not any other computational aids or electronic devices which transmit, receive, record or replay, etc.

• cross-reference all answer sheets to the questions and hand these in with your exam.• answers/calculations are complete only if the numbers are accompanied by units.• draw and use sketches freely to explain and support your calculations.• use the Tables in the Handbook to your advantage.• units are [mm] and [MPa] unless noted otherwise.• the exam consists of 3 questions (not all equal marks) and 4 pages for a total of 100 marks.

Question 1 (56 marks): BEAM-COLUMNThe WWF400x220 beam-column shown below is 20-metres high with lateral supports

only at the top and bottom. To eliminatebracing about the weak(y-y) axis, the cross-section has been reinforced with a pair ofW200x86 members which are boltedsomehow or welded to the web of theWWF400 sufficiently to achieve an integral/combined cross-section as shown (Figure1).y-y bending is not laterally suppressed alongthe height of the beam-column.The steel is ASTM A992, Fy=345 MPa.

______________________________________________● recall, for a W-shape (thin-walled open section with double symmetry):

Mu= (/L) √ E Iy G J + (/L)2 E2 Iy Cw

- if: 1 ≡ E Iy G J, and, 2 ≡ E2 Iy Cw

then, (/L)2= {-1 ±√ [12 + 4 2 Mu

2 ] } / (2 2)

- for a W-shape: Cw ≈ (Iflange h2 / 2) ≈ (Iyy-Beam h2 / 4) , and

J ≈ ⅓ b t3

Figure 1:Figure 1:

CE 470: Final Exam (11 December 2010) –Structural Steel Design(page 2/4)

Question 1: Beam-Column (questions for this built-up beam-column:)a) (18 marks) what are the section properties: A, Ixx, Iyy, rxx, ryy, Zxx, Zyy, …., J, and Cw ?b) (12 marks) according to Clause 13.3 (columns), calculate < Crx, Cry and Crz > .c) (4 marks) as a laterally-supported beam (Clause 13.5), calculate Mrxx and Mryy .d) (12 marks) as a laterally-unsupported beam (Clause 13.6), what values would you use

for Mr’xx, and Mr’

yy for unsupported compression-flanges of 20-metres? Mr’yy ≠ Mryy

e) (10 marks) finally, if used as a beam-column carrying biaxial end moments and an axialload, with notional loads for P- (sway) and P- (curvature) effects, with no transverseloads on this column, and 2nd-order bending moments as follows:

● about the xx-axis, the beam-column is part of a rigid frame (sway frame),(KL)xx=20,000 mm. The xx-axis bending moments are: Mf(xx-top)≈ ± 300 kN.m(f) at thetop, and Mf(xx-bott)≈ ±400 kN.m (f) at the bottom of the column.● about the yy-axis shown, the beam-column is in a braced frame (non-sway frame) and(KL)yy=20,000 mm with Mf(yy-top)≈ ± 280 kN.m(f), and Mf(yy-bott)≈ ± 350 kN.m(f).

Consider all 4 cases of Clause 13.8. Assume the built-up cross-section retains its shapeduring member buckling. Would you permit this built-up beam-column to carry an axialload of Cf =1000 kN according to S16-09? Assume the section is Class 2 or better.________________________________________________________________

• W400x220, CISC Handbook (page 6-36) section properties, page 4-118 Mr’xx, …

A= 28,000 mm2, Ixx= 834 x106 mm4, Iyy= 299 x106 mm4, rxx= 173 mm, ryy= 103 mm,Sxx= 4170 x103 mm3, Zxx= 4660 x103 mm3, Syy= 1490 x103 mm3, Zyy= 2260 x103 mm3,

J = 6320 x103 mm4 , Cw= 10,300 x109 mm6 …etc… (check Tables before using).

• for a single W200x86, the CISC Handbook (page 6-54):A= 11,000 mm2, Ixx= 94.7 x106 mm4, Iyy= 31.4 x106 mm4, rxx= 92.6 mm, ryy= 53.3 mm,Sxx= 853 x103 mm3, Zxx= 981 x103 mm3, Syy= 300 x103 mm3, Zyy= 458 x103 mm3,

J = 1390 x103 mm4 , Cw= 318 x109 mm6 …etc… (check Tables before using).

Areas=A1+A2+A3= 50,000 mm2Figure 1:

CE 470: Final Exam (11 December 2010) –Structural Steel Design(page 3/4)

Question 2 (20 marks): Composite Concrete-Steel Beam (Clause 17)A composite concrete-steel “twin beam” cross-section is shown below.Assume: fc’=25 MPa, Fy(steel beam)=345 MPa, bslab= 3 metres, t(deck)= 75mm, and

t(cover slab above the deck)= 65mm. The flutes (ribs) are to the beams.Shear studs at the concrete-steel interface connect the slab to a pair of W460x74 beams.Section properties of the steel beam are given on page 6-46 of the CISC Handbook.

1= 0.85 – 0.0015 (25 MPa) = 0.8125

Questions, for a 100% composite shear connection:a) calculate the location of the PNA (plastic neutral axis).b) calculate Mrc (composite section moment capacity).

Figure 2:

CE 470: Final Exam (11 December 2010) –Structural Steel Design(page 4/4)

Question 3 (24 marks): Short Answer Questions (marks as noted)a) (3 marks)- what purpose do Lu and Le serve for laterally-unsupported beams and at what

values of Mu do they occur in S16-09? Include a graphical sketch in your explanation.

b) (1 mark)- what is the baseline moment diagram for a point load at midspan for a simply-supported beam?

c) (1 marks)- what is a “half-space model” and when should its use be avoided?

d) (4 marks)- what is the difference between P- and P- effects in second-order analysis?What is the fundamental intent of “notional loads” in design codes? What magnitude ofnotional loads is used in CSA S16-09? What are the purposes of the numerator anddenominator terms in Clause 13.8.4 for calculating U1 for beam-columns?

e) (2 marks)- for welds, what’s all the fuss about in S16-09 regarding the factors:(1+0.5sin1.5θ), and, Mw?

f) (8 marks)- tell me all you know about “seismic design” rationale according to NBCC-2005and S16-09. Also, what are the names of the variables and graphs of “Sa(T) vs. T”, and“S(T) vs T”? What is the intent of application and what purpose do these graphs serve?

g) (5 marks)- for the two different W-shapes being circulated, (one painted green and theother blue), which one is most likely to be a “beam” section and which one a “column”section. Estimate/ measure the “b/t ratios” for each section and give each a “class”.

~ the end of CE470 and Good Luck as Engineers! ~