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HOMEWORK 5: Members subject to Axial Load and Bending
5.1
Write down the corresponding interaction equation(s) for the following load cases and determined the appropriate m-factors (mLT, mx or my) and the lengths for the evaluation of axial resistance, Pc and buckling resistance Mb.
(i)axial compression combined with major-axis moment as shown in Fig. Q5.1b.
(ii)axial compression combined with minor -axis moment as shown in Fig. Q5.1a
(iii)axial compression is zero; major-axis and minor-axis moments acting together (see Figs. Q5.1a&b).
5.2 Design a UC column of length 5 metre in S275 steel to resist the following factored loads: Factored axial load F = 1000kN; Factored Moments: Mx = 300kNm and My = 50kNm. Assume that the moments are applied at the top of the column. The bottom of the column is pin-connected. The effective length may be assumed to be 5m about both x- and y-axes. Check local capacity and overall buckling.
5.3 Check the suitability of a 533 x 210 x 82 UB in S355 steel for used as the column in a portal frames of clear height 5.6m if the factored axial compression force is 160kN, the factored moment at the top of the column is 530kNm and the base is pinned. Both ends of the column are adequately restrained against lateral displacement. If the UB section is not suitable, determine whether an intermediate lateral restraint located at 1.6m below the top of the column is sufficient to provide resistance for column buckling.
Fig. Q5.3
5.4 Select a suitable RHS in S355steel for the top chord of the 26.2m span truss shown below. Trusses are spaced at 6m intervals with purlins at 1.87m intervals; The trusses are prevented from lateral deflection at the top chord at these points. The factored loads acting on the chord member are compression F = 664kN; moments Mx = 24.4kNm, My = 19.6kNm.
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5.6A typical column in a multi-storey braced frame is subject to a compression force F = 610 kN and major-axis moments causing double-curvature bending Mx = 64 kNm as shown in Figure Q6. The column is laterally braced at the ends and at the mid-height. Assume that the ends are simply supported, design a suitable UC section for the column member and check its adequacy for strength and stability. (You may use the simplified method or the more exact approach for member capacity check).
CE 3164 Structural Steel Design:
SPECIAL PROBLEMS
5.7Design the beams and columns for the structure steelwork shown below.
Unfactored floor loading:
Imposed load = 5kN/m2; Dead load (including estimated self-weight) = 3kN/m2
Column tops are pinned connected to the beams.
Column bases are fixed.
All steels are grade 43.
Use UC and UB sections only.
Evaluate the two floor options and determine which option is more efficient in terms of steel usage.
Floor plans:
Option A
Option B
5.8Design the canopy system consisting of beam, column and tiefor the given loading shown below:
5.9Design the steel structure as shown below. The columns are of equal length inclined at 600 from the ground level and at a height of 5m. Compare the use of CHS and UC sections, assuming S275 steel.
P = dead load = 150kN; H = wind load = 75kN.
5.A portal frame, as shown in Fig. Q1a, is subject to gravity and wind load combination. The factored axial forces and moments in the members are shown in Fig. Q1b. The bases of the columns are simply supported, and the tops are braced against side sway. Assuming that lateral restraints are provided at Points B and C and C, design members AB and BC and check their local capacity and overall bucking resistance. (25 marks)
Hints: For member BC, use RHS 250x150 Grade 50 steel.
For member AB, use UC 203 x 203 Grade 43 steel
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Q5.10
A one-storey and two-bay frame consists of 9 floor beams, 6 columns and 3 bracing members are required to support a floor slab with unfactored dead load of 5 kN/m2 and imposed load of 3.5 kN/m2 as shown in Fig. Q5.10a. The dead load includes the self-weight of the steel structure. The column bases are assumed to be rigidly connected to the foundations. All other members are assumed to be pin-connected. The column top is braced to prevent side sway in the y-direction but is free to deflect in the x-direction causing major-axis bending. (Main Exam: 2001)
a)If the secondary beams are laterally restrained by the slab and the primary beam are laterally unrestrained, select one suitable UB section of S355 steel for both the primary and secondary beams and checks its bending and shear resistance.
b)Assuming that the column is subject to pure compression, select a suitable UC section S275 steel for the most critical column, and check its buckling resistance against the factored gravity loads.
5.11 A steel tower supports a water tank of size 4.5m x 2.5m x 3.0m is shown in Fig. 5.11. The self weight (DL) of the water tank is 60kN when empty. The column top is braced to prevent side sway in the y-direction but is free to deflect in the x-direction causing major-axis bending.
Assuming that weight of water (imposed load, IL) = 9.81 kN/m3, horizontal load is negligible and all steel sections are S275 43:
a)select a suitable UC section for the column member, and check its buckling resistance against the factored gravity loads (i.e., 1.4DL + 1.6 IL)
b)select a suitable RHS section for the beam, and check its bending and shear resistance
State your assumptions clearing with regard to the idealization of beam-to-column connections and column base connections.
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Dr Richard Liew CE3165 Structural Steel DesignC:\My Documents\CE3164\LecturerNotes\HW_05.doc