钢结构设计英文课程 助教课Tutorial 3_W2016 (Solution)

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Question I- Part 6 of the Handbook-Finding Properties of Sections For the following questions, write down the answer with units and the page in the handbook where you found it. 1) Find the cross-sectional area of a W200x59 wide flange section 2) Find the cross-sectional area of a WT100x29.5 T-section 3) Compare (1) and (2) and comment on the results 4) Without looking at the tables what is the depth and width of an HSS203x152x6.4. 5) Find the maximum moment of inertia for CSA G40.20 HSS203x152x6.4 Compare it to that of ASTM A500 HSS203x152x6.4 6) Find the distance between the shear centre and centroid of a C200x21 Solution 1) 7560 3780 2) 3) Notice that the area of WT100x29.5 is half the area of W200x59. Also the section designation is meant to represent the fact that the T section was cut from the W section. 203 4) 152 25 10 5) CSA G40.20 HSS203x152x6.4 22.9 10 ASTM A500 HSS203x152x6.4 6) The distance between the shear centre and the centroid of a C200x21 is shown in the handbook as 29.1 Question II- Radii of gyration for angles Angles are light members (economic) are commonly used as tension and compression members when the applied loads are not large. Their properties are listed in Pages 6-72 to 6-81 The minimum radius of gyration appears in many design requirements (tension members, compression members, etc.) For an L152x102x9.5 Determine the following 1) How many radii of gyrations are tabulated? 2) What are their values? 3) What are the angles of orientation of the principal axes? 4) Based on the above information, determine the minimum moment of inertia
2 Solution 1) Four 2) 48.9 , 29.8 , , 52.7 , , 22.4 3) Angle of orientation of principal axes, can be computed from provided in the handbook 0.451 24.3° 4)
Tutorial 3
(Solution) Introduction to the Handbook of Steel Construction
Objective: To familiarize students with the content of the handbook of steel construction
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Question VII on Part 1, and Appendices Part 1 consists of CAN/CSA S16-09 Limit States Design of Steel Structures (the code). These are a set of rules that a designer should comply with in his designs (a legal requirement). Appendices: At the end of Part 1, there are a set of Annexes. Unlike the standard, these are not all mandatory. Some are informal, suggested guidelines that the designer may comply with (or may opt for better solutions) and some are normative (a) How many Appendices are there? (b) Provide their titles Solution a) There are a total of 12 annexes, 10 of them being informative and 2 normative (Annex C and Annex K) b) Annexes are presented in pages 1-141 to 1-174
-0.15 0.175 0.10
-0.15 0.175
18.8 kNm + 21.9 kNm Example: 0.175 25 kN + 12.5 kNm 5m
18.8 kNm + 21.9 kNm
21.9 kNm
4 Question VI- Deflection of a beam Find the mid-span deflection of a prismatic beam of stiffness EI. The beam is simply supported at one end and is fixed at the other end and is subject to a uniformly distributed load w Solution: Mid-span deflection is not the maximum deflection given on page 5-149 for simply supported-fixed boundary conditions. In order to find the mid-span deflection, one must use the deflection equation for any point on the beam given in the handbook when x=l/2: ∆ 48 3 2 ∆ ∆ 48 2 3 . 2 2 2 2
3 a) For a W200x52, 5m long member, it is required to calculate the buckling loads. Young Modulus for the steel is E = 200, 000 MPa (Note: You need to extract the moments of inertia I xx , I yy from the table before you apply the above equation.) b) Given that the steel used is 380W , calculate its nominal (i.e., unfactored) yield resistance R = AFy (Note: You need to find the area of the section from the table. Also, you need to lookup the yield strength for 380W steel on Table 6.3 in your handbook). Solution a) 200,000 52.7 10 4161 10 4161 5000 200,000 17.8 10 1405 10 1405 5000 min , 1405 . b) 380 for 380 steel Table 6.3 handbook 6650 380 2527 10 2527 . Question V- on Part 5 of the Handbook - Analysis Aids: Section 5-146 to 5-164 Bending Moments for Statically indeterminate Beam A prismatic simply supported continuous beam has three equal spans of 5m each. Each span is subject to a concentrate load P=25kN acting at midspan. Draw the bending moments for the continuous beam. Solution: From page 5-161: Moment Coefficient W L where W The concentrated load on one span L Length of one span
,
that is being
22.4
,
Therefore: 2330 22.4 1.169 10 .
Question III- Key parameters for wide flange sections Wide flange sections are one of the most widely used sections in steel construction. They are commonly used as vertical columns or beams. Their properties are listed in Pages 6-40 to 6-55 The section designation signifies the following W310x129 W Wide flange section 310 Nominal height of the section in mm. 129 Weight in Kilograms per meter. Geometrically the section is completely defined using four parameters: 1) The section height d (close but not exactly identical to the nominal section height) 2) Web thickness w 3) The flange width b 4) The flange thickness t The above four parameters are defined in the diagram on top of the odd pages in your table a) For the above section, determine the value of each of the constants d, w, b, t h d − 2t b b) The ratios , = w w 2t are particularly important in designing columns and beams. For the given section, calculate these ratios. Solution a) 318 , 13.1 , 308 , 20.6 b) 2 277 21.15 13.1 308 7.48 2 20.6 2 Question IV- Ideal Resistance of a Column In your previous courses, you have learned that the elastic buckling resistance of a simply supported column of Span L , Young Modulus E and moment of inertia I is π 2 EI Pcr = 2 L