Arithmetical Calculations - Beam Framing - The Axial Load - Bending Moments - Engineering Assignment Help

Assignment Task:

1. Figure Q1 shows a steel column with eccentric loading, parallel to the axis of the column. The four beams framing into the top transmit factored at ULS point loads F1 = 130 kN, F2 = 170 kN, F3 = 65 kN and F4 = 280 kN, which are the support reactions correspondingly from beams B1, B2, B3 and B4 as shown. The indicated beams are on the top floor, no other axial load is applied to the column. The length of the column is 4 m and the column is laterally restrained at top and bottom with respect to buckling along y-y and z-z axes. It is effectively pinned on the top and at the bottom.

Check is UC 203x203x60 element suitable for such column conducting the following checks according to EC3:

(a) Calculate the axial load and the bending moments due to the eccentricities of applied forces. (4 marks)

(b) Calculate the total axial load and bending moments in both directions (the eccentricities to be calculated as appropriate). (5 marks) 1

(c) Calculate the compression buckling resistance (6 marks)

(d) Calculate the lateral-torsional buckling resistance and combined buckling resistance of the column.

2. The beam-to-column connection indicated in Figure Q2 is a ‘bolted end plate’ type of connection. It is designed to transfer vertical design load Ned, of 300 kN from the beam (UB356x171x67) to the column (UC254x254x73), both of which are made from S275 steel. The endplate size 240x160x10 is welded to the web of the beam and is made from S275 steel also (fu = 410 N/mm2 ).

The bolts are M20 HSFG bolts class 8.8 (fu = 800 N/mm2) and are positioned as indicated in Figure Q2. The distances are as follows: end distance e1 = 30 mm, edge distance e2 = 35 mm, pitch p1 = 60 mm and gauge p2 = 90 mm.

Check the following elements of the resistance of the ‘bolted end plate’ connection:

(a) Limitations for positioning of the holes. (8 marks)

(b) The bearing resistance of the bolt group assuming γM2 = 1.25. (10 marks) 2

(c) The shear resistance of bolt group with αv = 0.6.

3. A grade S355 steel beam 406x178x74 UB carries permanent loads and variable loads from two secondary beams as shown in Figure Q3. The beam is laterally restrained at the supports and the secondary beams. Design mineral fibre box protection to give 90min fire performance if the thermal properties of the proposed thermal insulation are as follows:

(a) Determine the design bending resistance of the beam at 20ºC temperature and compare with the design load at room temperature. (7 marks)

(b) Determine the critical temperature for the section. As a first iteration assume the critical temperature to be 550ºC. During the heating the variable action is to be considered as a quasi-permanent value ?Q where ? = 0.3 . (12 marks)

(c) Calculate the required minimum thickness of the protection to satisfy the required 90min of fire performance for the critical temperature. (6 marks)

4. A 3-spans continuous beam with two uniformly distributed loads and a point load is shown in Figure 4a. The cross section of the beam is made up of a UB strengthened with a plate on the top of the UB as shown in Figure Q4b. The yield stress of steel is 275N/mm2 .

(a) Determine Mp, the fully Plastic Moment, for the beam. (5 marks)

(b) Using Plastic Analysis method, investigate all possible collapse mechanisms and determine the actual collapse load and the corresponding collapse mechanism.(10 marks)

(c) For the collapse load in (b), draw the bending moment diagram showing all significant values.(10 marks)

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