IF SECOND-ORDER EFFECTS NEED TO BE CONSIDERED ON THIS EXAM, ASSUME A B1 MOMENT-MAGNIFIER OF 1.05.

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1 Name: E311 PST FINL EXMS You may use the Steel Manual, alculator, Drawing Supplies, only 100 points Given Steel Properties: E = ksi, G = ksi; 36 Steel (F y =36 ksi, F u =58 ksi); 992 Steel (F y =50 ksi, F u =65 ksi) Strength of Materials Formulae: Stress = E = G ending Flexural (normal) Stress M/EI = 1/ = -y/ =My/I M=EI I = ( /4)r 4 for a solid circular cross-section eam Shear Stress = VQ/It q = VQ/I q = F/s I = ( /4)r 4 for a solid, circular shape of radius r Torsional Formulae - J J Formulae for a losed Rectangle Reinforced oncrete: (psi) 1 depends on the strength of the concrete, as follows: If f c < 4 ksi, 1 = 0.85 If f c > 8 ksi, 1 = 0.65 If f c is between 4 and 8 ksi, then 1 = (8-f c) (units are ksi) 0.85 If b/t>10 J Formula for Open Sections, omposed of Thin Plates 1 3 J bt 3 Where b is the length of the long dimension of each plate and t is the thickness. Truss Degree of Indeterminacy: DOI = b + r 2j b = number of bars r = no. of reaction components j = number of joints IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF Page 1 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

2 ONUS QUESTIONS (0.1 points each): 1. Who was the only person to defeat Dan Gable in college? 1. (1 point) TRUE or FLSE. Group (325) S (Slip ritical olts) are made from a stronger high-carbon steel than Group (325) N bolts. 2. (1 point) The two tension connections shown have angles of the same gross area. The connections use the same diameter bolt holes. ircle the design that will be stronger with respect to bearing/tearout of the holes. 3. (2 points). olumns and have the same cross-section. olumn is 12 -long, while olumn is 7 -long. If olumn buckles elastically at an applied axial force P=100 kips, at what force does olumn buckle at, assuming it also buckles elastically? P=100 kips P=? 12 7 olumn olumn Page 2 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

3 4. (1 point) TRUE OR FLSE. The maximum axial force in the arch below occurs at Point. This is why traditional masonry arches have larger Keystones that are placed at the top of the arch. Given: the arch has a uniformly-distributed load. The arch has a parabolic shape and fixed supports at and. w = 1 kip/ft Solid Rock Foundation Solid Rock Foundation 5. (2 points). For which condition is the theoretical effective length factor K smaller in the vertical columns? W10x33 W36x652 W10x33 W10x33 W16x26 W10x () 40 () 6. (2 points) The structure has the connections indicated. Determine the degree of indeterminacy (DOI) of the structure then state whether it is stable or not. roller pin pin pin pin pin pin pin pin pin pin DOI = Stable? 7. (2 points) What is the degree of indeterminacy of the structure below? ll beam-column connections are rigid. ll foundations are pins. DOI = Page 3 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

4 8. (2 points) For the frame shown, what is the theoretical K value for column? Given: Fixed base (foundation), rigid (moment-resisting) column-girder connections. Girder is W16x26. olumn is considered to have infinite EIx. W16x26 EIx = infinite K = 9. (3 points) Estimate the deflection for Open-Web Girder Number 2. Given: It is known that Open-Web Girder Number 1 has a midspan deflection of 1 inch. Open-Web Girder Number 2 has the same loading and utilizes the same sized flanges, but has a depth of 9, rather than a depth of 6. Uniform Load Uniform Load 6 9 L Open-Web Girder Number 1 Open-Web Girder Number 2 L Girder Number 2 Deflection = 10. (7 points) Determine the maximum normal stress magnitude in the structure below, due to the point loads. Given: Points and D are fixed foundations; points and are rigid connections. ll members are made from hollow square tubing 4 x4 outside dimensions with ½ wall thickness. 5 kips 5 kips ½ D Member ross-section Page 4 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

5 11. (4 points) For eam, determine the vertical reactions at,, and eam w = 0.1 kips per inch Given: If the beam has support removed, then the deflection at is If the beam has support removed, and a 1 kip force is applied at, then the deflection at is w = 0.1 kips per inch = , 1 kip = (2 points). If all of the connections in the frame are pins and the floors act as diaphragms, then (ircle the correct answer):. olumn is considered unbraced with K=1. olumn is considered braced with K>1. olumn is considered braced with K=1 D. olumn is considered unbraced with K>1 Page 5 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

6 13. (6 points) ccording to SD, what is the maximum total uniform load (resultant force) that the 992 W16x31 may safely sustain if it is subjected to a uniformly distributed load in weak-axis bending over the 12-foot span shown, with bracing at the midpoint and at the supports? Do not consider deflection. ircle the closest answer. race X X X 6 feet 6 feet ). 188 kips ). 106 kips ). 90 kips D) kips E) kips F) kips 14. (12 points). Select the lightest 992 W shape for girder that is safe per SD, considering bending moment, only. Given: The floor plan shown. Members are pin-ended, in strong-axis bending. The members shown support a 4 -thick concrete slab ( concrete = 150 lb/ft 3 ). Use a live load of 75 psf (the live load reduction factor has already been applied) Do not consider shear or deflection. 20 W16x26 30 W18x35 W16x26 20 Floor Plan 15. (15 points) The pin-connected truss is loaded (SD loads), as shown. If Member is an HSS 4x4x3/8, determine if it is adequate per SD. Given: Preferred material specification for HSS tubing is F y =46ksi 2 kips/ft Page 6 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

7 16. (8 points) The building shown is laterally braced by concrete shear walls on the outside of the building. The floors act as diaphragms (omitted for clarity). The foundations and all connections are pins. The story heights are 16 ft. If column must be designed for an axial force from Dead = 150kips, Live = 100kips, and Snow = 60kips, select the lightest 992 W10 shape for that is adequate per SD. Note how the concrete wall is built into the web of column. ol Page 7 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

8 17. (15 points) Member of the truss shown is a double angle 2L2½ x2x 3/16 LL 36 member, connected with (3) 5/8 Group N bolts, in standard holes. Determine if it is adequate per SD, considering Yield, Fracture, and olts, only. You may use either method for the shear lag factor, U, but clearly indicate which was used kips 20 kips 20 kips /8 SETION a-a a a DETIL 18. (15 points). Use the Principle of Virtual Work to determine the deflection at Point due to the concentrated endmoments. Given: oncentrated moment M = 1 kip-ft at point. oncentrated moment M = 16 kip-ft at point. EI = 1000 kip-ft 2 M = 1 kip-ft 5 ft 10 ft M = 16 kip-ft Page 8 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

9 ONUS QUESTIONS (0.1 points each): 1. Who coached the Iowa Hawkeyes to 15 N Team hampionships in wrestling between 1976 and 1997? MTH THE QUOTE TO ITS UTHOR. W.T. Sherman If the N was on channel 5 and a bunch of frogs making love was on channel 4, I'd watch the frogs even if they were coming in fuzzy.. Leonardo da Vinci On a neutral field, Germany ETS Russia. Vince Lombardi hurchill was no alcoholic, for no alcoholic could drink that much D. Robert Hooke Give me fifty men who aren't afraid to die, and I can take any position. E. William F. uckley, Jr. When you are playing for the national championship, it's not a matter of life or death. It's more important than that. F. uthor Unknown If I owned both Hell and Texas, I d rent out Texas and live in Hell G. The Terminator lways go to other people's funerals, otherwise they won't come to yours. H. Socrates. You just have to learn to sleep less I. Dan Gable I swear it upon Zeus an outstanding runner cannot be the equal of an average wrestler. J. Duffy Daugherty You may beat me, but you will not outwork me K. "Yogi" erra When I read about the evils of drinking, I gave up reading L. Henny Youngman s hangs a flexible cable, so, inverted, stand the touching pieces of an arch. Perfection is unattainable but if we chase perfection, we may M. John Lennon catch excellence N. John L. Kurtz, Sr. Life is what happens to you when you're busy making other plans O. Plato God sells us all things at the price of labor. P. obby Knight nger is more useful than despair Q. eano ook I d rather be governed by the first hundred names in the telephone directory than by one hundred faculty at Harvard Who s this Rorschach guy and why is he so good at drawing R..P. Snow pictures of my mom beating me? S. John K. Wells He was a wise man who invented beer Page 9 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

10 Engineering onus Question:. (2 points). The steel (E=29000ksi, G=11200ksi) I-shape is subjected to end torques that cause a twist angle of radians over its length of 100 inches. Determine the applied torque, T (units: kip-in). 100 T 10 x ½ Flange 10 x ½ Web 10 x ½ Flange T T = Page 10 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

11 1. (2 points). For which condition is the theoretical effective length factor K smaller in the vertical columns? W10x33 W16x26 W10x33 W10x33 W36x652 W10x () 40 () 2. (2 points) The structure has the connections indicated. Determine the degree of indeterminacy (DOI) of the structure then state whether it is stable or not. See Detail DOI = Stable? Detail: Shear Tab (plate) is welded to the column and connected to the web of the beam. The flanges (top and bottom plates) of the beam are not connected 3. (2 points) The structure has the connections indicated. Determine the degree of indeterminacy (DOI) of the structure then state whether it is stable or not. 10 ft 1 k/ft 10 ft 5 ft D 15 ft DOI = Stable? E Page 11 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

12 4. (5 points) Determine the maximum compressive stress in member E if it is a W10x33, oriented as shown 1 k/ft D 10 ft 10 ft 5 ft 15 ft E Maximum compressive stress 5. (3 points). What is the vertical component of force y at Point? Given: Parabolic arch with fixed supports, a uniformly-distributed load of w=1 kip/ft, and a maximum arch height of 5. w = 1 kip/ft w = 1 kip/ft 5 feet y =? x 8 feet The Given Problem 4 feet ut at 6. (4 points) ircle the correct P n / for the 992 W12x210 column kips P P kips kips 6 race D. 450 kips 18 6 race 6 P P View 1 View 2 Page 12 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

13 7. (15 points). Determine if the W21x57 member EH has adequate moment resistance, per SD. Given: Floor framing supports a 4 -thick concrete slab ( concrete = 150 lb/ft 3 ), cast on metal decking that was welded to the top flanges of the beams. Use a live load pressure of 80psf (assume that the live load reduction was already applied, resulting in 80psf). The area bounded by DE is a floor opening (no slab or beams). ll connections are pins. Page 13 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

14 8. (12 points) Select the lightest 992 W8 shape for column grid location 2, between the foundation and the 2 nd floor. Two-story building, shown. Story Heights: 20 ll connections are simple pins. The floors act as rigid diaphragms. The column is subjected to axial forces, only. Roof Dead Load Pressure = 25 psf. This includes every dead load on the roof (framing, decking, roofing material, etc). 2 nd Floor Dead Loads: W16x26 Fill eams and W18x35 Girders, as shown, supporting a 4-inch-thick concrete ( = 150 lb/ft 3 ) slab. Live Load, FTER pplying the Live Load Reduction Factor: 80 psf. (it has already been applied. Do not apply it again). Snow Load: 100 psf (location: rctic ircle) (15 points) Per SD specifications, determine the maximum force P that may be safely applied to the top of the cantilevered column shown, below. The force is applied with a 1 foot eccentricity as shown in View 1. Given: The column is an 992 W16x77. For the K-value, use the Recommended design value when ideal conditions are approximated. For second-order effects, assume a Moment Magnifier 1 =1.05 (do not perform any actual second-order analysis). P P 1 Load is applied here 12 ft. 1 Top View View 1 View 2 Page 14 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

15 10. (5 points). Steel ridge onnection. 1 square tube with a wall thickness of is sandwiched by two plates, connected by a ¼ bolt that goes through a drilled 9/32 hole (because the hole is not punched, no damage is associated with the hole). The tube has a yield strength F y = 60 ksi and an ultimate strength of F u =70 ksi. The ¼ diameter bolt has an ultimate tensile strength F u =150ksi. The bolt is tightened to a pretension of 0.5 kips. ssume the Shear Lag Factor is 0.6. Determine the Nominal Fracture Strength R n of the tube. Rn R n SIDE VIEW ½ ½ ROSS SETION 11. (5 points). The Manslaughter Problem Determine the Nominal Tearout Strength R n for the previous problem. 12. (12 points) Use the Principle of Virtual Work to determine the vertical deflection of point due to the 5 kip load. EI = 1,000,000 kip-in P=5 kips 13. (4 points) For eam, determine the vertical reactions at Page 15 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

16 eam w = 1 kip per foot Given: If the beam has support removed, then the deflection at is 0.5 If the beam has support removed, and a 1 kip force is applied at, then the deflection at is 0.04 w = 1 kip per foot = , 1 kip = (8 points) Using I (merican oncrete Institute) methods, determine M n for the reinforced concrete beam crosssection, shown, which contains 6 No. 4 tension bars (f y = psi) and uses concrete with a compressive strength f c =3000psi. The beam is subjected to positive bending (6 points) ccording to SD, what is the maximum total uniform load (resultant force) that the 992 W16x31 may safely sustain if it is subjected to a uniformly distributed load in weak-axis bending over the 12-foot span shown, with bracing at the midpoint and at the supports? Do not consider deflection. ircle the closest answer. 10 race X X X 6 feet 6 feet ). 188 kips ) kips ) kips D) kips E). 106 kips F). 90 kips Page 16 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

17 1. (3 points). What is the degree of indeterminacy (DOI) of the frame shown? ll supports are pinned. The diagonal brace is pin-ended. The beam to column connections are as shown in the Detail. See Detail Detail: Shear Tab (plate) is welded to the column and connected to the web of the beam. The flanges (top and bottom plates) of the beam are not connected DOI of the frame, as shown. DOI = 2. (2 points) For the plane shown, what is the theoretical K value for column? Given: W12x40 columns, W24x103 girder, pinned base (foundation), pinned (non-moment-resisting) column-girder and brace connections. Page 17 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

18 3. (22 points). SD. Determine the most severe load combination and the corresponding load on column 2 at the base of the building. Then, determine the allowable load P n / on that column and specify whether or not the column is safe. Do apply the live load reduction factor (it has already been applied) onsider all given dead loads Use Exact K Values Given: Dead Loads: ll columns are W10x77. ll fill beams are W18x35. ll girders are W24x55. The second floor slab is 6 thick (unit weight of concrete is 150 lb/ft 3 ). The roof is composed of corrugated metal decking and standard roofing materials that apply a total pressure of 14 psf, not including the weight of fills or girders. 2 nd Floor Live Load: 60 psf (do not use the live load reduction factor: assume it has already been applied, giving a value of 60 psf, for this problem). Roof Loads: No snow (location: Southern Florida). Roof live load: 20 psf. onnections: For one direction, the beam-column connections are moment resisting.. ll other connections are pins North Roof 2 nd Floor Plan View Roof 2 nd Floor Elevation View Looking from East to West Elevation View Looking from South to North Page 18 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

19 4. (7 points). ircle the correct answer. The nominal strength P n for an 992 W14x145 in axial compression with KL x = 24 and KL y = 12 is (to 3 digits of precision): kips kips kips D. 872 kips E kips F. None of the bove 5. (2 points). TRUE or FLSE. ¾ Group Slip ritical bolt has the same nominal strength with respect to the bolt shear limit state as a ¾ Group N bolt. 6. (7 points). Using IS, determine the force P that will cause the collapse of the 992 W8x58. ssume that the beam self-weight is negligible. Given: raced at the end-points, only. ircle the closest answer ) kips ) kips ) kips D) kips E) kips race P race 8 feet 8 feet 7. (3 points). TRUE or FLSE. The hypothetical 992 rolled wide-flange beam shown has continuous lateral support of its compression flange and flange slenderness that is exactly equal to r. This implies that, for strong-axis bending, local buckling would be the controlling limit state with the extreme tips of the flanges just reaching yield, when this occurs. Flange = r Page 19 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

20 8. (16 points) Determine the maximum load P that the 13 -long 992 W16x36 pin-ended beam-column can safely support per SD specifications. Given: equal-magnitude strong-axis end-moments of 10 ft-kips, and equal-magnitude weakaxis end-moments of 2 ft-kips, as shown. The column is in a braced frame, braced at its ends, only, for both axes. ssume that self-weight is negligible. ssume that the 1 factor is 1.05 for strong-axis moment and 1.10 for weak-axis moment. P =? kips P =? kips M = 10 ft-kips M = 2 ft-kips 13 feet 13 feet M = 10 ft-kips M = 2 ft-kips P =? kips View 1 P =? kips View 2 9. (2 points). beam is shown below, along with the Influence Line for Internal ending Moment at Point. Explain what the -3.5 value means. D INFLUENE LINE FOR MOMENT T (KIP-FT) 10. (13 points) Determine the maximum magnitudes of positive and negative bending moments that are possible at point Given Dead Load 1 kip/ft distributed load Live Load 1 kip/ft distributed load Live Load 10 kip point load Page 20 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

21 11. (15 points) Use the Principal of Virtual Work to compute the horizontal deflection of point on the structure shown below. Given: is a fixed foundation. is a rigid beam-column connection. EI = 10,000,000 kip-in 2 w = 0.1 kip/inch (8 points). mong the many wonderful failure modes that Dragon Fire dodged or succumbed to was this one, shown below. Determine the force that must have been present in the girder tubing at the instant of failure using IS specifications (do not include, however. We want to know the actual force in the flange). Given: 1 x1 ( wall thick.) square tube, connected with ¾ x 1/8 side plates and ¼ diameter bolts Tubing and plate material: Yield and ultimate tensile strengths - F y = 60 ksi, F u = 75 ksi olt: Ultimate tensile strength F u = 120 ksi 1/8 thick plate 1x1 Tube ( wall) ¼ diameter hole 3/8 3/8 3/8 3/8 ½ ½ PHOTO OF FILURE ONNETION DETIL Page 21 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

22 1. (13 points) Use the Principle of Virtual Work to compute the vertical deflection at point due to the w=0.1kip/inch uniformly distributed load. The beam is fixed at and D. and are pinned connections. EI=10,000,000kip-in 2. Given: the horizontal reactions at and D will be zero. w=0.1kip/inch D (13 points) Determine the maximum P that may be safely applied per SD to the 992 W16x57 shape, if it is applied as two equal point-loads P/2, as shown. Second order effects: assume that the second order moment magnifier 1 is Given: The 10 -long 992 W16x57 shape is simply supported with lateral bracing at the supports and at the point loads, only; the lateral bracing prevents the beam from moving laterally (in or out of the page) at those points, only. It is subjected axial compression of 300 kips. Do not consider self-weight separately (it will be assumed that the self-weight of the W16x57 is approximately lumped into the unknown concentrated forces). P/2 =? P/2 =? race 300 kips race W16x57 race race 300kips 10 - feet 10 - feet 10 - feet 3. (2 points). Determine the degree of indeterminacy (DOI) of the structure below: DOI = 4. (2 points). Determine the degree of indeterminacy (DOI) of the structure below: DOI = 5. (2 points). Determine the degree of indeterminacy (DOI) of the structure below: DOI = Page 22 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

23 6. (1 point) TRUE or FLSE. If the loads P were increased until failure occurred, the structure below would fail because the entire structure is unstable. P P P P Indicates pin (or momentrelease) Indicates rigid (or momentresisting) connection. 7. (2 points). olumns and have the same cross-section. olumn is 10 -long, while olumn is 6 -long. If olumn buckles elastically at an applied axial force P=100 kips, at what force does olumn buckle at, assuming it also buckles elastically? P=100 kips P=? 10 6 olumn olumn 8. (2 points) Is the following beam-column connection simple (non-moment-resisting) or rigid (moment resisting) for strong-axis bending? Given: the wide-flange beam is connected to the column-face with a bolted angle. There is an unconnected space between the beam flange and the face of the column. nswer (ircle or ) olted angle connection. Simple (non-moment-resisting). Rigid (moment resisting) 9. (2 points) Show why the structure below is indeterminate, but unstable. 10. (1 point) TRUE or FLSE. The LRFD design buckling load P n is larger than the SD allowable buckling load P n / P allow because the LRFD method is less conservative. Page 23 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

24 11. (1 point) TRUE or FLSE. For the rigid frame shown below, the K value for the columns is less than one. 12. (1 point) TRUE or FLSE. For the frame below, column is considered braced, but column is considered unbraced. Page 24 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

25 13. (2 points). For the column application below, the structure consists of 1 x1 thin-walled top and bottom tubes that are loaded in compression. The tubes are joined together with diagonal web members, as shown. The entire structure is 12-feet long, pinned on both ends. Question: if the top and bottom tubes were to be replaced with rectangular tubes having the same cross-sectional area as the current design, which orientation (circle one) would be the more efficient? P 1x1 tube P P x1 tube If rectangular tubes (of the same cross-sectional area) are substituted for the 1 x1 inch tubes shown, which is the more efficient orientation for the rectangular tubes (circle one): () () 14. (1 point) TRUE or FLSE. The structure below is an arch. P 15. (1 point) TRUE or FLSE. Given the same loads, a bolted connection that uses Group (325) N bolts requires a greater number than a connection that uses the same sized Group (325) S bolts. Page 25 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

26 16. (8 points). Select the lightest W shape that is adequate, using the SD method. lso, explain why this is a completely idiotic bracing design. Given: ll connections are pinned. s shown below, bracing is provided at the ends and at the midpoint for strong-axis buckling, but only at the ends for weak-axis buckling. P Dead = 100 kips, P Live = 500 kips, P Snow = 250 kips P P (10 points) IF THE FOLLOWING PROLEM N E SOLVED WITH STTIS, determine the maximum stress in member. First, determine if the problem can be solved by statics, alone (if it cannot be solved by statics, show why this is the case); then, if it can be solved, determine the stress in member. Given: fixed foundation supports. The cross-section of the arch consists of a 6 x6 solid, made from timber. 5 kips 5 kips D 5 kips 4 ft. 8 ft. E 10 ft. 20 ft. 20 ft. 10 ft. 6 x6 Timber (wood) ross Section 18. (7 points) Specify the required minimum cable diameter for the main cable if the allowable tensile stress is 50 ksi. w = 500 lb/ft Page 26 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

27 19. (10 points). Referring to the building below, determine the magnitude of force on the brace along column line, between 1 and 2, between the 2 nd floor and the Roof, for an applied wind pressure of 20 psf (the actual pressure is 33.3psf, but the SD factor for wind is 0.6, so use 20 psf), directed from South to North and state whether the member is in tension or compression, in this case. NORTH Roof 2 nd 12 Ground D View of uilding 3D View, Showing raced ays, Only Note: vertical exterior wall studs, spaced 16 apart, are omitted, for clarity. ll connections are Simple (non-moment-resisting). The floors are considered to be diaphragms. Page 27 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

28 20. (5 points) ½ diameter bolt was tested in tension, failing at a load of kips. Three (3) ¾ diameter bolts from the same manufacturer, manufactured from the same steel (assume the strength is identical) will be used in a double shear application, as shown, and threads will not be excluded from the shearing planes. Determine: P n / for the bolted connection, assuming that bolt shear controls. ross- Section Side View 21. (3 points) Problem: For the 70 kip applied (SD) load, specify the number of ¾ Group (325) N bolts needed for the connection shown, considering bolt shear, only. Given: 2L4x4x1/4 36 double angle with a ½ thick gusset plate. Single line of bolts is assumed. ` Single olt Line 70 kips Section 22. (1 point) For which double-angle connection is shear lag a more serious problem (i.e., leads to a lower fracture strength), assuming the gross areas are the same? 23. (4 points) What is the fracture strength of the 2L5x3x1/4 36 double-angle tension member, if a single line of (4) ¾ bolts in standard holes is used? The spacing between each bolt is 3. Note the orientation of the angles. Page 28 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

29 24. (6 points) ompute the plastic moment capacity M p of the section shown for STRONG-XIS ENDING. The beam is built-up out of 12 x1 flange plates and a 12 x ½ web plate. ll plates are ½ Page 29 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

30 ONUS QUESTIONS 1. (3 points) Legitimate bonus question. Determine the magnitude of the reaction components x and D x, specifying their directions. w = 0.1kip/inch 200 inches 500 inches D Given: Two analyses have already been done (shown below). On the left, the given frame was analyzed while turning the pin at D into a roller and the result was that the roller would move inches to the right. On the right, the given frame was analyzed with a roller at D and a 1 kip force applied at D, as shown, with the result that the roller would move inches to the left. w = 0.1kip/inch 200 inches 200 inches 500 inches D 500 inches 1 kip D From an analysis using The Principal of Virtual Work, roller D moves inches to the right From an analysis using The Principal of Virtual Work, roller D moves inches to the left. Page 30 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

31 North Roof 18 2 nd Floor D Final Exam uilding 4 uilding Description: ll connections are simple (non-moment-resisting pins). The floor and roof act as diaphragms. The second floor slab is 5 inches thick (concrete unit weight is 150 lb/ft 3 ) and is cast on metal decking that was welded to the top flanges of all beams and girders. The roof is metal deck that was welded to the top flanges of the beams and girders (it is considered sufficient to offer full lateral bracing and act as a diaphragm). Loads: Wind pressure in SD is 20 psf (the actual code wind pressure is an ultimate pressure of 33.3psf, but the SD load factor for wind is 0.6, so use 20psf in an SD design). Roof dead load is 25 psf and includes the weight of beams, girders, and all other aspects of the roof level dead loads. 2 nd floor live load: 100 psf Roof snow load: 80 psf (Northern laska) The second floor dead load is from the slab weight given, but you must also consider the weights of beams, girders, and columns. For preliminary load estimation: you may assume that all columns weigh about 50 lbs per linear foot. The exterior wall consists of studs that span from floor to floor, as shown. Their weight and the weight of the exterior wall is considered negligible. The building has four braced bays: long, between 2 and 3, along D, between 2 and 3, along 1, between and, and along 4, between and. Page 31 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

32 1. (10 points) Referring to the Final Exam uilding, select the lightest possible typical interior 24 -long fill beam for the 2 nd floor with SD specifications, using an 992 wide-flange (W) shape in strong-axis bending. ssume that deflection and shear are not a concern because the span is neither very long nor very short. e sure to include all relevant dead loads. 2. (10 points) Referring to the Final Exam uilding, select the lightest possible typical interior girder for the 2 nd floor with SD specifications, using an 992 wide-flange (W) shape in strong-axis bending. ssume that deflection and shear are not a concern because the span is neither very long nor very short. e sure to include all relevant dead loads. If you have not done problem 1 yet, you may simply assume that the fill beams weigh 35 lbs per linear foot. 3. (10 points) Referring to the Final Exam uilding, select a column for grid location 3 based on the loads present at the base of the building with SD specifications, using an 992 wide-flange (W) shape. e sure to include all relevant dead loads. If you have not done problems 1 and 2, you may simply assume that the fill beams weigh 35 lbs per linear foot and girders weigh 80 lbs per linear foot. 4. (10 points) Referring to the Final Exam uilding, select an adequate member for the brace along column line, between column lines 2 and 3, assuming that the braces are considered to be redundant, tension-only braces; use SD specifications to select an 36 single-angle tension member that is adequate for the yielding limit state then specify the number of 5/8 diameter 325-N ( Group ) bolts that are needed for the applied load. 5. (17 points) Determine the vertical movement of point due to the applied loads, using the Principle of Virtual Work. Given: Pinned support at, roller support at, rigid connection at. Uniform load of 1 kip/ft from to. 2 kip point load at the midspan of. EI = kip-ft 2. 1 kip/ft 2 kip 10 ft. 5 ft. 5 ft. 6. (2 points) For column buckling, what is the theoretical K value for column if beam has infinite flexural stiffness? Given: pinned base supports, rigid beam-column connections. EI => D Page 32 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

33 7. (2 points) For column buckling, what is the theoretical K value for column if beam has zero flexural stiffness? Given: pinned base supports, rigid beam-column connections. EI is 0 D 8. (2 points) For column buckling, what is the theoretical K value for column if beam has zero flexural stiffness? Given: fixed base supports, rigid beam-column connections. EI is 0 D 9. (2 points) For column buckling, what is the theoretical K value for column if beam has infinite flexural stiffness? Given: pinned base supports, rigid beam-column connections, pin-ended brace between and. EI => D 10. (2 points) What is the degree of indeterminacy of the structure below? ll beam-column connections are rigid. ll foundations are pins. Page 33 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

34 11. (6 points) Two views of the same 992 W10x54 column are shown. ircle the closest answer. P n / P n / 6 ft ). Pn/ = 83.4 kips 6 ft ). Pn/ = 446 kips 36 ft races 6 ft 6 ft ). Pn/ = 232 kips D). Pn/ = 261 kips 6 ft 6 ft 12. (6 points) n 992 W16x26 is subjected to equal end moments in weak axis bending, as shown. It is braced at its ends, only. ssume that self-weight is negligible. ircle the closet answer. Mn/ Mn/ 8 feet ). M n / = 110 kip-ft ). M n / = 13.7 kip-ft ). M n / = 86 kip-ft D). M n / = 22.8 kip-ft Page 34 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

35 13. (15 points) Per SD specifications, determine the maximum force P that may be safely applied to the top of the cantilevered column shown, below. The force is applied with a 1 foot eccentricity as shown in View 1. Given: The column is an 992 W16x77. For the K-value, use the Recommended design value when ideal conditions are approximated. For second-order effects, assume a Moment Magnifier 1 =1.05 (do not perform any actual second-order analysis). Note: b is equal to 1 for any cantilever. Hint: Initially assume that the 8/9 interaction expression will be applicable, then verify that this is true, at the end. P P 1 Load is applied here 12 ft. 1 Top View View 1 View (6 points) n 992 W16x26 beam is spans 10 feet, subjected to a center-point load P. It has continuous lateral bracing. ssuming self-weight is negligible, circle the closest answer for the maximum P that may be safely applied, per SD. P ontinuous lateral bracing W16x26 5 feet 5 feet ). Maximum safe P = 88.2 kips ). Maximum safe P = 33.2 kips ). Maximum safe P = 44.0 kips D). Maximum safe P = 22.0 kips Page 35 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

36 1. (15 points) Determine the maximum axial compression P that may be safely applied per SD to the 992 W18x35 shape. Second order effects: assume that the second order moment magnifier 1 is Given: The 10 -long 992 W18x35 shape is simply supported with lateral bracing at the supports, only. It is subjected to strong-axis bending due to a uniformly distributed load w=2 kip/ft, which already includes self-weight. It is also subjected to axial compression, P. w = 2 kip/ft race P W18x35 race P 10 - feet 2. (2 points) TRUE OR FLSE. Point can have negative internal moment but can never have positive internal moment Given: The beam may be loaded with the following Dead Load 1 kip/ft distributed load Live Load 1 kip/ft distributed load Live Load 8 kip point load D (2 points) ircle the correct answer. ll members are rigidly-connected. Supports are pins ). The structure is an arch, it has a Degree of Indeterminacy of 1, but can be solved by Statics because it is funicular. ). The structure is not an arch, it has a Degree of Indeterminacy of 1, and cannot be solved by Statics because it is indeterminate. ). The structure is an arch, it has a Degree of Indeterminacy of 3, but can be solved by Statics because it is funicular. D). The structure is not an arch, it has a Degree of Indeterminacy of 0 and can be solved by statics because it is determinate. 5 kips 5 kips (1 points) TRUE or FLSE. races are designed as axially-loaded two-force members. 5. (1 points) TRUE or FLSE. The SD method will lead to larger (bigger, stronger) member selection than LRFD when live loads are relatively high and dead loads are relatively low. Page 36 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

37 6. (2 points) For the plane shown, what is the theoretical K value for column? Given: Fixed base (foundation), rigid (moment-resisting) column-girder connections. Girder is W16x26. olumn is considered to have infinite EIx. W16x26 EIx = infinite 7. (2 points) For the plane shown, what is the theoretical K value for column? Given: W12x40 columns, W24x103 girder, pinned base (foundation), simple (non-moment-resisting) column-girder connections. 8. (2 points) Given: For a certain column, it is known that the column has 205 and applied axial loads Ω consist of 10 kips of dead load and 190 kips of live load. Is the column safe, per LRFD? Justify your answer. 9. (2 points) TRUE or FLSE. The external virtual work is the work done by a real force, as this real force moves through a virtual displacement. 10. (3 points) What does it mean if a steel section is non-compact for bending? 11. (2 points) TRUE or FLSE. The Maximum Total Uniform Load Tables (Table 3-6, IS) account for the reduction in strength that is attributable to lateral-torsional buckling. 12. (2 points). TRUE or FLSE. Local buckling cannot occur if a beam is bent about its weak axis. 13. (2 points) TRUE or FLSE. The allowable compressive force for column will become greater if beam is increased in size (increased moment of inertia). ll connections are simple pins. P P D Page 37 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

38 14. (2 points) What is the degree of indeterminacy of the structure below? ll beam-column connections are rigid. ll foundations are pins. 15. (4 points) Given: The single-story building shown has a rigid roof diaphragm. ll member connections are pinned Determine the horizontal reaction component for the base of column 3, due to 20psf wind pressure, directed in the y-direction. (circle one): a. 2.5 kips b. 0 kips c. 20 kips d kips e. 5 kips f. 10 kips g kips y x D Page 38 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

39 16. (24 points) Part ). Determine the horizontal movement of point due to the applied loads on the frame below (labeled Part using the Principle of Virtual Work. Given: EI is constant. w = 1 kip/ft Part Part ). Use an exact indeterminate analysis to plot the moment diagram for the indeterminate frame, shown below, left (standard sign convention: plot on the compression side). Given: The frame has the same EI as the Part Frame. lso, an analysis was performed on the frame shown, below right, which concluded that point would move a distance of 6666/EI (units: kips, ft) to the left if a 1 kip force was applied to point, directed to the left. w = 1 kip/ft 1 kip Part (Problem) Part Given: Point Would move 6666/EI feet to the left due to the 1 kip force) Page 39 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

40 17. (10 points) Determine the normal stress at position due to the applied load at D and clearly indicate whether this stress is tensile or compressive, where position is located 5 feet up from position, on the left-hand side of the column,. The column is a hollow 12 x12 square tube with a wall thickness of ½, as shown. 10 kip E loseup Detail of Point (point is on the lefthand extreme fiber of the hollow square tube column) D 6 ft ft ft 4 ft 4 ft olumn ross Section 12 x 12 Hollow Square Tube w/ ½ Wall Thickness 18. (14 points) Select the lightest 992 wide-flange (W-shape) for a typical interior girder, assuring that it is safe per SD, considering shear, bending moment, and live load deflection (L/360 limit). Given: eams and girders are in strong-axis bending. The beams and girders support a 5 thick normal weight concrete (unit weight = 150 lb/ft 3 ) slab, which continuously braces the top flanges of the beams, laterally. The fill beams weigh 35 lbs per linear foot. Loads to onsider: Slab Weight, eam Self-Weight, and a live load of 100 psf. Notes: ll connections are simple, non-moment-resisting. ssume that the slab provides full lateral support of the compression flange. 34, typ 28, typ FLOOR PLN Page 40 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.

41 19. (4 points) n 36 (F y = 36 ksi) W16x26 is subjected to equal end moments in weak axis bending, as shown. It is braced at its ends, only. ssume that self-weight is negligible. ircle the closest answer. Mn/ Mn/ 8 feet ). M n / = 110 kip-ft ). M n / = 13.7 kip-ft ). M n / = 86 kip-ft D). M n / = 22.8 kip-ft E). M n / = 9.84 kip-ft 20. (4 points) n 992 W16x26 beam spans 10 feet, subjected to a center-point load P. It has continuous lateral bracing. ssuming self-weight is negligible, circle the closest answer for the maximum P that may be safely applied, per SD. P ontinuous lateral bracing W16x26 5 feet 5 feet ). Maximum safe P = 88.2 kips ). Maximum safe P = 33.2 kips ). Maximum safe P = 44.0 kips D). Maximum safe P = 22.0 kips Page 41 IF SEOND-ORDER EFFETS NEED TO E ONSIDERED ON THIS EXM, SSUME 1 MOMENT-MGNIFIER OF 1.05.