Q1. The simply supported frame ABCD shown on Figure Q1 is…

Q1. The simply supported frame ABCD shown on Figure Q1 is made from steel grade S275. It is subjected to the following nominal loads: horizontal point load F at the support at point D with magnitude 30 kN as permanent load and 40 kN as variable load. In addition uniformly distributed load w acting downwards is applied on the horizontal part BC of the frame with magnitude 120 kN/m as permanent load and 140 kN/m as variable load.

Evaluate the loading on the top of the vertical part AB. Assume that the column is supported by pinned supports top and bottom and loaded on compression and uniaxial bending. The height of the column AB is 4 m. Check the adequacy of UC 254x254x132 column for the load effects from simultaneous action of indicated loading in ULS.

Perform the following design calculations based on EC3:

(a) Calculate the design values for bending and compression load effects acting at the top of the column AB assuming all loads applied simultaneously. (4 marks)

(b) Check the resistance of the existing cross section of the column at point B to bending and compression. (6 marks)

(c) Check the buckling resistance of the column AB about the major and the minor axes. (5 marks)
(d) Check lateral torsional buckling and combined buckling effects.
(10 marks)

B
C
D
A
Figure Q1

Continued …

Q2. Check if a baseplate 500x500x35 mm given in Figure Q2 is suitable to resist an axial design load, Ned, of 2700 kN. Assume that the foundations are of concrete of compressive cylinder strength, fck, of 30 N/mm2 and that the baseplate is made of grade S275 steel. The universal column section welded centrically to the baseplate is UC305x305x118.

Check the total resistance of the base plate following the steps indicated below:
(a) Calculate the additional bearing width x and check if the size of the plate is sufficient to accommodate it.
(8 marks)

(b) Calculate the effective area of the plate and check if the axial load capacity of the baseplate is sufficient.
(8 marks)

(c) Calculate the moment of resistance of the baseplate and check it against maximum bending moment per unit length of the plate.

(9 marks)

Figure Q2.

Continued …

Q3. A steel beam 406x178x60 UB (grade S355) is simply supported over a span of 4.5m and is only laterally restrained at the supports. Determine the critical temperature of the unprotected beam if the characteristic values of the uniformly distributed load are gk=20 kN/m and qk=25 kN/m. Calculate the required minimum thickness of the mineral fibre board protection on 4 sides of the beam to provide fire resistance time of 60min.

Figure Q3

Mineral fibre board properties:
λp=0.25 W/mK
cp=1500 J/kgC
ρp=500 kg/m3

(a) Determine the flexural capacity of the 406x178x60 UB at ambient temperature considering the LTB of the beam according to the ULS.
(10 marks)

(b) Carry out the corresponding SLS check of the moment capacity of the steel beam using the factor to determine the critical temperature of the section.
(10 marks)

(c) Calculate the minimum required thickness of the protection, if the fire resistance time is 60min.
(5 marks)

Continued …

Q4. The following rigid-jointed and fixed-base frame is subjected to working loads as shown in Figure Q4:

(a) Draw the possible collapse mechanisms and determine the critical collapse load Pc (in terms of Mp and L);
(15 marks)

(b) Prove that Pc is the true unique collapse load;
(5 marks)

(c) Draw the bending moment diagram at critical collapse load Pc.
(5 marks)