CES 4605 Structural Steel Design Dept. of Civil EngineeringFlorida Atlantic University

Summer 2007

Mid-Term Examination

Name:--------------------------------------------------

June 25 , 2007 Instructor: Dr. M.Arockiasamy

Time: 1 Hour

SOLUTIONS

Part I: Closed Book

Answer all Questions

Credit will be given to clarity of presentation

Show all your step by step calculations or as much details as possible wherever necessary

1. A column in the upper story of a building is subject to a factored load of 214.4 kips. Given the resistance factor = 0.90, what is the required nominal strength?

Ru ≤ Rn

214.4 ≤ 0.90Rn

Rn 238 kips

2. If the column in Problem 1 were to have a required service load strength of 158.5 kips, and the safety factor Ω = 1.67, what is the required nominal strength?

Ra ≤ Rn / Ω

158.5 ≤ Rn / 1.67

Rn 265 kips

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3. Explain the Load and Resistance Factor Design.

LRFD is similar to plastic design. Failure condition is considered. Load factors are applied to the service loads.Factored load Factored strength

4. Name an important factor in the design of cold-formed steel structures.

Instability arising from the thinness of cross-sectional elements

5. Name the two limit states to be considered in the design of a steel tension member.

Excessive deformation initiated by yielding or fracture

6. Distinguish between the net area , gross area and effective net area of a tension member connected at the ends by bolts to a gusset plate.

net area = reduced area due to the presence of the holes

gross area = unreduced area

effective net area accounts for shear lag effects in both bolted and welded connections

7. Explain by a neat sketch the phenomenon of block shear in the connection of a single – angle tension member.

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8. Explain the basis for AISC B4 “Classifications of Sections for Local Buckling”

Limiting values of width-thickness ratios of the elements of the cross-section are given in AISC B4. The cross-sectional shapes are classified as compact, noncompact, or slender according to the values of the ratios.

9. How do you account for the strength of a compression member with thin flanges or webs likely to have local buckling.

The strength is reduced by a reduction factor, Q

10. How do you provide additional resistance to lateral loads to a frame with moment-resisting joints?

Diagonal bracing or rigid shear walls

11. Explain by a neat sketch the type of failure in a compression member with one axis of symmetry ( e.g., channels, structural tees )

The member bends and twists simultaneously.

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12. Explain the concept of plastic analysis.

13. The rigid frame shown in Fig. is unbraced. Each member is oriented so that its web is in the plane of the frame. Determine the effective length factor Kx for column BC. Given G = Ic/Lc / Ig Lg . The following properties are given:

Shape Ix-x (in.4 )W12x120 1070W24x55 1350W24x68 1830

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14. Distinguish between yield moment and plastic moment. For these two cases, sketch the stress distributions in the cross section of a simply supported W-shape beam with a concentrated load at midspan.

yield moment, My = Fy Sx

plastic moment., Mp = Fy Zx

15. What are the three possible failure modes of beams of compact shapes?

a. Lateral –torsional buckling (LTB) either elastically or inelasticallyb. Flange local buckling (FLB) either elastically or inelasticallyc. Web local buckling(WLB) either elastically or inelastically

16. The tension member shown in Fig. is a plate ½ x 8 of A36 steel. The member is connected to a gusset plate with 1.125 in diameter bolts. It is subjected to the dead and live service loads shown. Does this member have enough strength as per LRFD and ASD?. Assume that Ae = An . Given Fy = 36 ksi; Fu = 58 ksi; and

Pu 0.90 Fy Ag

Pu 0.75 Fu Ae

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For tensile yielding in the gross section, Ωt = 1.67For tensile rupture in the net section, Ωt = 2.00

Pn = 58 x 3.375 = 195.75 kipsASDPa = 95 + 9 = 104 kipsPn / Ωt = 195.75/ 2.0 = 97.87 kips Pa = 95 + 9 = 104 kipsMember does not have enough strength as per ASD

17. A simply supported W 14x90 beam has a span of 40 ft carrying a uniformly distributed load and is laterally supported at its ends. Given the limiting laterally unsupported lengths Lp and Lr are respectively 15.2 and 42.6 ft, comment on the bending strength and the type of failure of the beam.

Since Lp = 15.2 Lb = 40 ft Lr = 42.6 ft

Failure will be due to Inelastic Lateral Torsional Buckling

18. For the beam in Problem 17, = bf /(2tf) = 10.2 . Given the parameter p = 0.38 (E/Fy) and r = 1.0 (E/Fy), Fy = 50 ksi and E = 29,000 ksi, Is this shape compact, noncompact or slender?

p = 0.38 (E/Fy) = 0.38 x (29000/50 ) = 9.15

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r = 1.0 (E/Fy) = 24.08

Since p = 9.15 = 10.2 r = 24.08, this shape is noncompact.

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