CN228 Design of Structural Steel Members 2012-13
School of Environment & Technology
Semester 1 Examinations 2012-2013
CN228
DESIGN OF
STRUCTURAL STEEL MEMBERS
Instructions to Candidates
Time allowed: TWO hours
Answer FIVE questions from a total of SIX
Total mark of this exam
(each question 20 marks)
(100 marks)
An Aide Memorie is provided
Monday 28th of January 2013, 9:30hours
Page 1 of 12
CN228 Design of Structural Steel Members 2012-13
Question 1 (total mark = 20)
(1-A) The required plastic modulus based on the design bending moment of
a simply supported restrained beam (fully restrained against lateral torsional
buckling) under uniformly distributed load is 530 cm3. Determine two closest
UKB trial cross-sections that have enough ultimate bending resistance to
withstand this bending moment. If there is a maximum height restriction for
this beam in the roof, which one of those cross-sections would you choose? (7 marks)
(1-B) The required area of the cross-section design based on the design force
of a short/stub column is 47 cm2. Determine two closest UKB trial cross-sections
that have enough ultimate tensile resistance to withstand this axial force. This
member is embedded in a wall. If there is a maximum width restriction of the
wall, which one of those cross-sections would you choose?
(7 marks)
(1-C) The required second moment of area of a cantilever restrained beam
(that is covered by plaster of brittle finish) subjected to an un-factored imposed
point-load at the end is 4400 cm4 to satisfy the serviceability limit state.
Determine the closest UKB trial cross-section that satisfies the serviceability
limit state.
(6 marks)
Question 2 (total mark = 20)
The end plate shown in Figure Q2 is subjected to a tensile axial load and is 20 mm
thick; and contains four lines of staggered holes drilled for 24 mm bolts; where its
yield strength is fy = 275 N/mm2 and its ultimate strength is fu = 430 N/mm2 .
(2-A) Calculate the ultimate tensile resistance of the plate (based on the
probable failure modes).
(10 marks)
(2-B) Identify whether 14 non-preloaded Class 4.8 M24 diameter bolts can
provide enough shear resistance to transfer this ultimate tensile force. (6 marks)
(2-C) Determine the required length of a-(6 mm)-fillet-weld to transfer this
ultimate tensile force if the end plate is welded (instead of being bolted).
(4 marks)
Figure Q2
Page 2 of 12
CN228 Design of Structural Steel Members 2012-13
Question 3 (total mark = 20)
A 406 X 178 X 74 UKB (cross sectional properties on the next page) is designed as
an unrestrained beam, which is subjected to equal end bending moments about its
major axis. Length of the beam between points of lateral restraint (pinned at both
ends) is Lcr = 4.5 m. Assuming the overall cross-section classification is “Class 1 in
bending” and all partial safety factors for resistance are
M =1.0 :
(3-A) Select the appropriate section modulus for this cross section Wy .
(2 marks)
(3-B) Calculate elastic critical moment for lateral torsional buckling Mcr .
(4 marks)
(3-C) Work out the non-dimensional lateral torsional slenderness
(3-D) Determine reduction factor for lateral torsional buckling

 .
LT
(3 marks)
LT
– please note that
buckling curve (a) is recommended for this cross-section.
(7 marks)
(3-E) Calculate lateral torsional buckling resistance of this member Mb,Rd.
(4 marks)
Question 4 (total mark = 20)
A 406 X 178 X 74 UKB (cross sectional properties on the next page) is used as a
beam that is bending about its strong axis (assume that the overall cross-section
classification is Class 1 in bending and the beam is fully restrained against lateral
torsional buckling):
(4-A) Determine shear area of the cross section (Av).
(3 marks)
(4-B) Calculate shear resistance of the cross-section (Vpl, Rd).
(4 marks)
(4-C) Calculate the maximum bending resistance of this section if the design
shear force in the section is 50 kN.
(6 marks)
(4-D) Calculate the maximum bending resistance of this section if the design
shear force in the section is 50 kN and the design axial load is 25 kN. (7 marks)
Question 5 (total mark = 20)
A 406 X 178 X 74 UKB (cross sectional properties on the next page) is used as a 4.5
m column that is fully restrained against buckling about its weaker axis and free to
buckle about the other axis (assuming the cross-section is fully effective in
compression - Class 1 or 2):
(5-A) Identify effective length of the column if its end conditions are free-fixed. (2 marks)
(5-B) Calculate elastic critical buckling load.
(4 marks)
(5-C) Determine non-dimensional slenderness (  ).
(3 marks)
(5-D) Calculate flexural buckling reduction factor () – please note that buckling curve
(b) is recommended for this cross-section when buckling about y-y axis.
(7 marks)
Page 3 of 12
CN228 Design of Structural Steel Members 2012-13
(5-E) Calculate flexural buckling resistance of the cross-section (Nb, Rd).
(4 marks)
Page 4 of 12
CN228 Design of Structural Steel Members 2012-13
Cross sectional properties for the questions 3, 4 and 5
b
z
tw
h
d
y
y
r
tf
406 × 178 × 74 UKB rolled beam
z
c
Depth of cross section
Web depth
Width of the flange
Web thickness
Flange thickness
Flange outstand
Root radius
Web depth between fillets
Second moment of Area
Radius of gyration
Elastic section modulus
Plastic modulus
Warping Constant
Torsional Constant
Section area
Modulus of elasticity
Shear Modulus
Nominal yield strength of steel
h
= 412.8 mm
hw = h – 2 tf
b
= 179.5 mm
tw = 9.5 mm
tf
= 16.0 mm
c
= 0.5 [ b – (tw + 2 r)]
r
= 10.2 mm
d
= 360.4 mm
Iy
= 27310 x 104 mm4 & Iz = 1545 x 104 mm4
iy
= 17 mm
& iz
= 4.04 mm
3
3
Wel,y = 1323 x 10 mm
& Wel, z = 172 x 103 mm3
Wpl, y = 1501 x 103 mm3
& Wpl, z = 267 x 103 mm3
12
6
Iw
= 0.608 x 10 mm
It
= 62.8 x 104 mm4
A
= 9450 mm2
E
= 210 000 N/mm2
G
= 81 000 N/mm2
fy = 355 N/mm2
Question 6 (total mark = 20)
Describe the failure mode of the sections shown in the following five photographs;
(6-A)
An Angle (L-shaped connector) –
connecting web of a beam to flange of a column (4 marks)
Page 5 of 12
CN228 Design of Structural Steel Members 2012-13
………………….. Questions 6 continues on the next page …………….
Questions 6 continued
(6-B)
I-shape beam (4 marks)
(6-C)
Top of an I-shape column (4 marks)
(6-D)
A simply supported I-shape beam (4 marks)
(6-E)
An I-shape beam (4 marks)
Page 6 of 12
CN228 Design of Structural Steel Members 2012-13
SAL BEAMS
(assume all Sections Class 1 in bending)
nce UKB
z
y
perties
s
z
y
z
Plastic
Modulus
Axis
Axis
y-y
z-z
Buckling Torsional Warping Torsional
Parameter Index
Constant Constant
U
X
3
cm 3
cm 3
6
6
5
9
5
2
0
0
3
9
2
5
5
2
2
0
2
7
711
614
539
481
403
342
566
483
393
353
306
259
314
258
234
171
123
84.2
116
0.873
23.3
98.4
0.872
26.5
85.4
0.872
29.7
60.0
0.867
31.6
48.4
0.859
37.3
38.8
0.846
43.4
141
0.891
21.1
119
0.890
24.3
94.1
0.879
29.6
BS EN 1993-1-1:2005
54.8
0.873
27.5
BS 4-1:2005
46.0
0.866
31.4
37.3
0.856
36.3
88.2
0.882
21.5
70.9
0.876
25.6
49.7
0.888
22.4
41.6
0.886
22.6
31.2
0.890
19.5
22.6
0.894
16.3
Area
of
Section
Iw
dm6
IT
cm 4
A
cm 2
0.102
0.0846
0.0725
0.0442
0.0349
0.027
0.103
0.0857
0.0660
0.0280
0.0230
0.0182
0.0374
0.0294
0.0154
0.0099
0.00470
0.00200
31.8
21.1
14.8
12.2
7.40
4.77
23.9
15.3
8.55
9.57
6.42
4.15
10.3
5.96
7.02
4.41
3.56
2.85
61.2
53.4
47.2
41.8
35.9
31.6
54.8
47.2
39.7
36.1 UNIVERSAL BEAMS
32.0
28.0
Advance UKB
38.2
32.0
29.4
24.3
20.3
16.5
z
y
Properties
elationship between Universal Beams (UB) and the Advance range of
Section
Second Moment
Radius
Designation
of Area
of Gyration
Axis
Axis
Axis
Axis
y-y
z-z
y-y
z-z
305x127x48
305x127x42
305x127x37
305x102x33
305x102x28
305x102x25
254x146x43
254x146x37
254x146x31
254x102x28
254x102x25
254x102x22
203x133x30
203x133x25
203x102x23
178x102x19
152x89x16
127x76x13
cm 4
cm 4
9570
8200
7170
6500
5370
4460
6540
5540
4410
4000
3410
2840
2900
2340
2100
1360
834
473
461
389
336
194
155
123
677
571
448
179
149
119
385
308
164
137
89.8
55.7
cm
12.5
12.4
12.3
12.5
12.2
11.9
10.9
10.8
10.5
10.5
10.3
10.1
8.71
8.56
8.46
7.48
6.41
5.35
cm
2.74
2.70
2.67
2.15
2.08
1.97
3.52
3.48
3.36
2.22
2.15
2.06
3.17
3.10
2.36
2.37
2.10
1.84
y
z
Elastic
Modulus
Axis
Axis
y-y
z-z
Plastic
Modulus
Axis
Axis
y-y
z-z
cm 3
cm 3
cm 3
cm 3
616
534
471
416
348
292
504
433
351
308
266
224
280
230
207
153
109
74.6
73.6
62.6
54.5
37.9
30.5
24.2
92.0
78.0
61.3
34.9
29.2
23.5
57.5
46.2
32.2
27.0
20.2
14.7
711
614
539
481
403
342
566
483
393
353
306
259
314
258
234
171
123
84.2
116
98.4
85.4
60.0
48.4
38.8
141
119
94.1
54.8
46.0
37.3
88.2
70.9
49.7
41.6
31.2
22.6
Buckling Torsional Warping Torsional
Parameter Index
Constant Constant
Area
of
Section
U
X
Iw
dm 6
IT
cm 4
A
cm 2
0.873
0.872
0.872
0.867
0.859
0.846
0.891
0.890
0.879
0.873
0.866
0.856
0.882
0.876
0.888
0.886
0.890
0.894
23.3
26.5
29.7
31.6
37.3
43.4
21.1
24.3
29.6
27.5
31.4
36.3
21.5
25.6
22.4
22.6
19.5
16.3
0.102
0.0846
0.0725
0.0442
0.0349
0.027
0.103
0.0857
0.0660
0.0280
0.0230
0.0182
0.0374
0.0294
0.0154
0.0099
0.00470
0.00200
31.8
21.1
14.8
12.2
7.40
4.77
23.9
15.3
8.55
9.57
6.42
4.15
10.3
5.96
7.02
4.41
3.56
2.85
61.2
53.4
47.2
41.8
35.9
31.6
54.8
47.2
39.7
36.1
32.0
28.0
38.2
32.0
29.4
24.3
20.3
16.5
Advance and UKB are trademarks of Corus. A fuller description of the relationship between Universal Beams (UB) and the
Advance
Page
7 ofrange
12 of
sections manufactured by Corus is given in section 12.
FOR EXPLANATION OF TABLES SEE NOTE 3