ADVANCED STRUCTURAL DESIGN

EXAM COVER SHEET School of Computing, Engineering & Digital Technologies Module Title: ADVANCED STRUCTURAL DESIGN Module Code: CEN4029-N

RESIT Tutor Name:

Time of Exam:

Location:

Begin Reading Time:

Begin Exam Time:

End Exam Time:

Duration of Exam:

09:00 (11/08/20) – 16:00 (12/08/20) Names of Students

(if split over more than one venue)

INSTRUCTIONS TO CANDIDATE(S):

1.

MCQ Exam?

YES

NO

2.

Case study?

YES

NO

3.

Open Book Exam Format?

YES

NO

4.

Dictionaries permitted?

YES

NO

5.

Calculators can be used?

YES

NO

Where YES only the below models are permitted

Casio FX-991EX CLASSWIZ

Casio fx991 (EX, ES or ES-PLUS models)

Casio fx85-(ES or GT-PLUS models)

Casio fx83-(ES or GT-PLUS models)

Casio FX-9750GII Graphic Calculator

Texas Instruments TI-83, TI-84 Graphic Calculator

6.

Can students retain the exam paper

YES

NO

Insert additional instructions below: This paper consists of FOUR questions of which you should attempt THREE. All questions carry equal marks. All answers must be written in an answer book. A formula sheet is included at the end of the examination paper.

Page 2 of 12

Question 1

Consider the building which has a plan and a section view as shown in Figure Q1.1, and perform the following tasks:

a) Estimate the characteristic external wind pressures acting on the windward side wall for a wind blowing in the y–axis of the building using the EN1991-1-4 provisions. Provide a sketch indicating the distribution of the wind pressures along the height of the building.

Consider also the following: (i) Ignore the effect of internal pressures. (ii) The fundamental value of wind velocity before altitude correction (𝑣𝑏,𝑚𝑎𝑝) =25𝑚𝑠𝑒𝑐⁄. (iii) The altitude of the building site is 40m. (iv) Also, assume that the ground surface on the site is flat (i.e. no topography effects). (v) The relevant terrain category of the building is II.

[14 marks]

(a)

(b)

Figure Q1.1: (a) Plan view and (b) Section A – A of the building

b) Evaluate the design snow pressure and total design snow force acting on the roof of the building, if it is situated on the south-east coast of UK. Sketch the snow distribution.

[5 marks]

c) Provide in a sketch, qualitatively, the wind velocity profiles for two different terrain categories (0 and III). Explain in which terrain the wind forces acting on a same structure will be larger and why. You can support your answer using sketches and/or equations.

[6 marks]

d) The same building (denoted as building 2) is situated in two different sites (site 1 and site 2) as shown in Figure Q1.2. The two sites have the same altitude and zone number. Explain in which one of the two cases a larger snow load should be expected and why. How is this taken into account in the relevant Eurocode (EC1 Part 1.3)?

[5 marks]

(a)

(b)

Figure Q1.2: Building 2 in (a) Site 1 and (b) Site 2

Wind direction

Wind direction

X

X

Y

Y

2

20m0m

15m

15m

A

A

A

A

15

15mm

15m

15m

1

1

2

2

3

3

1

1

2

2

3

3

Page 3 of 12

Question 2

a) Explain the use and meaning of the following two equations for the combination of loads and describe each one of the terms. What is the meaning of the ‘+’ sign in these equations.

[8 Marks] Σ𝛾𝐺,𝑗𝐺𝑘,𝑗𝑗≥1"+" 𝛾𝑃𝑃 "+" 𝛾𝑄,1𝑄𝑘,1"+"Σ𝛾𝑄,𝑖𝜓0,𝑖𝑄𝑘,𝑖𝑖>1 Σ𝐺𝑘,𝑗𝑗≥1"+" 𝑃 "+" 𝑄𝑘,1"+"Σ𝜓0,𝑖𝑄𝑘,𝑖𝑖>1

b) Consider the pin – supported frame which is under a permanent point load 𝐺𝑘, a variable line load 𝑞𝑘 and a wind load 𝑃𝑘 as shown in Figure Q2.1. Using the load combination equation for the ultimate limit state, estimate the design reactions at support E and identify the most unfavourable load combination case. Please make use of the information provided in Table Q2.1 and the formula sheet. Ignore the self-weight of the members. The I-cross-sections are oriented in such a way so bending occurs about their strong axis (see Figure 2.1(a)).

[15 Marks]

(a) Wind Load, Pk

(b) Uniform Line Load, qk

(c) Point load Gk at mid-span

𝑅𝐴=𝑅𝐸=𝑃𝑘ℎ𝐿Τ⁄

𝑅𝐴=𝑅𝐸=𝑞𝑘𝐿2Τ⁄

𝑅𝐴=𝑅𝐸=𝐺𝑘2Τ⁄

𝐻𝐴=𝐻𝐸=𝑃𝑘2Τ⁄

𝐻𝐴=𝐻𝐸=𝑞𝑘𝐿4𝑒ሺ(2𝛽𝑒+3ሻ)

𝐻𝐴=𝐻𝐸=3𝐺𝑘𝐿8ℎሺ(2𝛽𝑒+3ሻ)

Figure Q2.1: Vertical and horizontal support reactions for three different load cases.

L

L

R

RAA

R

REE

P

Pkk

A

A

B

B

D

D

E

E

H

HAA

H

HEE

h

h

R

REE

R

RAA

A

A

D

D

E

E

B

B

q

qkk

H

HAA

H

HEE

C

C

R

REE

R

RAA

A

A

D

D

E

E

B

B

G

Gkk

H

HAA

H

HEE

Page 4 of 12

Table Q2.1: Design data Description Symbol Units Magnitude

Frame height

h

m

4

Frame width

L

m

8

Wind point load

Pk

kN

50

Permanent point load on beam BD

Gk

kN

100

Variable line load on beam BD

qk

kN/m

40

Beam section (see formula sheet for properties)

UB 686x254x152

Column section

UC 356x406x634

Combination factor for variable action P (wind)

ψ0

[-]

0.6

Combination factor for variable action q (imposed)

ψ0

[-]

0.7

c) Classify the two beam – column connections given in Figure Q2.2 based on strength and stiffness considerations. By using hand-drawn sketched, describe qualitatively the moment – rotation (M-φ) behaviour for each one of the two connections and explain which would be more appropriate for the frame details given in question 2(b).

[7 Marks]

(a)

(b)

Figure Q2.2: Beam – column connections (a) and (b)

Page 5 of 12

Question 3

a. Provide a brief description for at least three considerations of the considerations which a designer must take into account during the conceptual design phase of a building frame comprising of shear wall systems. You may use hand-drawn sketches to aid your explanations.

[7 Marks]

b. In tall building design, Framed-tube systems are often used. Explain the main advantages and challenges of using framed-tube system in a tall structural system.

[7 Marks]

c. What are the emerging trends in tall building design to enhance sustainable features in tall structures? Support your answer with examples.

[8 Marks]

d. Explain why damping is important for tall structural systems and how damping can be increased in a tall structural system.

[8 Marks]

Page 6 of 12

Question 4

a. Using a simplified approach to the ‘Strut and Tie Model’, design the pile cap shown in

Figure Q4 for tension reinforcement. Total depth of the pile cap is 1400mm and breadth

is 900mm. The pile cap is supporting a 500mm square column carrying 2000 kN of

factored load and is supported by two piles of 600mm diameter at 1800mm centre-tocentre

spacing. The characteristic strength of the concrete used for the pile cap (fck) is

40 MPa and the grade of reinforcement steel is 500 MPa. Any assumptions made in

the design process must be stated clearly. You need to perform the necessary checks

as required by Eurocode.

Figure Q4

[18 Marks]

a. Describe why ‘Strut and Tie model’ can be used for the design of deep beams.

[6 Marks]

b. Describe the main factors which contribute to the selection of mat foundations for

tall buildings?

[6 Marks]

2700 mm

1400

mm

150 mm

2000 kN

Page 7 of 12

Formula sheet

Wind loading

𝐹𝑤=𝑤𝑒𝐴𝑟𝑒𝑓

Total wind force acting on a wall face

𝑤𝑒=𝐶𝑝𝑒𝑞𝑝

External wind pressure on a wall face

𝜌=1.25𝑘𝑔𝑚3⁄

Air density

𝑞𝑝(𝑧)=(1+7𝐼𝑣(𝑧))12𝜌𝑣𝑚2(𝑧)

Peak wind pressure

𝐼𝑣(𝑧)=1𝐶𝑜𝑙𝑛(𝑧𝑧0⁄)

Turbulence intensity

𝑘𝑟=0.19(𝑧0𝑧0,𝐼𝐼)0.07

Terrain factor

𝑐𝑟=𝑘𝑟𝑙𝑛(𝑧𝑧0)

Roughness factor

𝑣𝑚=𝑐𝑟(𝑧)𝑐𝑜(𝑧)𝑣𝑏

Mean wind velocity

𝑣𝑏=𝑐𝑑𝑖𝑟𝑐𝑠𝑒𝑎𝑠𝑜𝑛𝑣𝑏,0

Fundamental value of the basic wind velocity

𝑣𝑏,0=𝐶𝑎𝑙𝑡𝑣𝑏,𝑚𝑎𝑝

Basic wind velocity

𝐶𝑎𝑙𝑡=1+0.001𝐴

Correction factor to consider actual altitude of the site

Table: Recommended values for external pressure coefficients Zone A B C D E

h/d

𝑐𝑝𝑒,10

𝑐𝑝𝑒,10

𝑐𝑝𝑒,10

𝑐𝑝𝑒,10

𝑐𝑝𝑒,10

5

-1.2

-0.8

-0.5

+0.8

-0.7

1

-1.2

-0.8

-0.5

+0.8

-0.5

≤0.25

-1.2

-0.8

-0.5

+0.7

-0.3

Figure: Zone distribution for the Cpe external pressure coefficients

A.2 Transition between roughness categories 0, I, II, III and IV

If the structure is situated near a change of terrain roughness at a distance:

- less than 2 km from the smoother category 0

- less than 1 km from the smoother categories I to III,

the smoother terrain category in the upwind direction should be used.

Page 8 of 12

𝒉>𝟐𝒃

NOTE: The rules for the velocity pressure distribution for leeward wall and sidewalls (zones A, B, C and E) may be given in the National Annex or be defined for the individual project. The recommended procedure is to take the reference height as the height of the building.

Terrain category

z0 (m)

zmin (m)

0

Sea or coastal area exposed to the open sea

0.003

1

I

Lakes or flat and horizontal area with negligible vegetation and without obstacles

0.01

1

II

Area with low vegetation such as grass and isolated obstacles (trees, buildings) with separations of at least 20 obstacle heights

0.05

2

III

Area with regular cover of vegetation or buildings or with isolated obstacles with separations of maximum 20 obstacle heights (such as villages, suburban terrain, permanent forest)

0.3

5

IV

Area in which at least 15 % of the surface is covered with buildings and their average height exceeds 15 m

1.0

10

E.1.2 Criteria for vortex shedding

(1) The effect of vortex shedding should be investigated when the ratio of the largest to the smallest crosswind dimension of the structure, both taken in the plane perpendicular to the wind, exceeds 6.

z

zee=h=h

q

qpp((zz)=q)=qpp(h)(h)

Building face

Building face

z

z

h

h

b

b

Reference

Reference heightheight

h

h

q

qpp((zz)=q)=qpp(b)(b)

h

h--bb

z

zee==bb

Building face

Building face

z

z

b

b

b

b

Reference

Reference heightheight

q

qpp((zz)=q)=qpp(h)(h)

z

zee=h=h

h

h

q

qpp(z)=q(z)=qpp(b)(b)

b

b

Building face

Building face

z

zee=b=b

b

b

b

b

Reference

Reference heightheight

q

qpp(z)=q(z)=qpp(h)(h)

z

zee=h=h

𝒃<𝒉≤𝟐𝒃

𝒉≤𝒃

Page 9 of 12

(2) The effect of vortex shedding need not be investigated when

𝑣𝑐𝑟𝑖𝑡,𝑖>1.25𝑣𝑚

where: 𝑣𝑐𝑟𝑖𝑡,𝑖 is the critical wind velocity for mode i, as defined in E.1.3.1

𝑣𝑚 is the characteristic 10 minutes mean wind velocity specified in 4.3.1 (1) at the cross section where vortex shedding occurs (see Figure E.3).

F.2 (2) The fundamental flexural frequency n1 of multi-storey buildings with a height larger than 50 m can be estimated using Expression (F.2): 𝑛1=46ℎ [𝐻𝑧]

where: h is the height if the structure in m

E.1.3.1 Critical wind velocity 𝒗𝒄𝒓𝒊𝒕,𝒊

(1) The critical wind velocity for bending vibration mode I is defined as the wind velocity at which the frequency of vortex shedding equals the natural frequency (mode i) of the structure or the structural element and is given in Expression E.2). 𝑣𝑐𝑟𝑖𝑡,𝑖=𝑏∙𝑛𝑖,𝑦𝑆𝑡

where:

b is the reference width of the cross – section at which resonant vortex shedding occurs and where the modal deflection is maximum for the structure or structural part considered; for circular cylinders the reference width is the outer diameter.

ni,y is the natural frequency of the considered flexural mode I of cross-wind vibration; approximations for n1,y are given in F.2

St is the Strouhal number as defined in E.1.3.2.

Snow loading

𝑠𝑘=0.14𝑍−0.1+𝐴501⁄

Characteristic snow load in UK in kPa

𝑠=𝜇𝑖𝐶𝑒𝐶𝑡𝑠𝑘

Snow load on roof in kPa

Snow load shape coefficients

Angle of pitch of roof α

00≤𝑎≤300

300<𝑎<600

𝑎≥600

𝜇1

0.8

0.8(60−𝛼)30⁄

0.0

𝜇2

0.8+0.8𝛼30⁄

1.6

-

Figure: Snow load shape coefficients - pitched roof

Figure: Snow load shape coefficients - monopitch roof

Page 10 of 12

Buckling of struts

𝜎𝑚=𝑃𝐴+(𝑃𝐸𝑃𝐸−𝑃)𝑐𝑎𝐼𝑃

Maximum stress at a distance c from the neutral axis of a section in any direction

𝑧=𝑃𝑃𝛦−𝑃𝛼

Total lateral deflection of the mid – span of a strut

𝑃𝐸=𝜋2𝛦𝛪𝐿2⁄

Euler buckling load for a pinned supported strut

𝑃=(−𝛽̅±√𝛽̅2−4𝛼̅𝛾̅)2𝛼̅⁄

Solutions of the quadratic equation 𝛼̅𝑃2+𝛽̅𝑃+𝛾̅=0

Load combination equations

Σ𝛾𝐺,𝑗𝐺𝑘,𝑗𝑗≥1"+" 𝛾𝑃𝑃 "+" 𝛾𝑄,1𝑄𝑘,1"+"Σ𝛾𝑄,𝑗𝜓0,𝑖𝑄𝑘,𝑖𝑖>1

Load combination equation for the ultimate limit state design

Σ𝐺𝑘,𝑗𝑗≥1"+" 𝑃 "+" 𝑄𝑘,1"+"Σ𝜓0,𝑖𝑄𝑘,𝑖𝑖>1

Load combination equation for the serviceability limit state design

Safety factors

Table: Partial safety factors for loads in serviceability and ultimate limit states

Limit state

Partial safety factor for permanent actions Gk

Partial safety factors for variable actions Qk

ULS

𝛾𝐺=1.35

𝛾𝑄=1.50

SLS

𝛾𝐺=1.00

𝛾𝑄=1.00

Indeterminate frame

Page 11 of 12

Where 𝑒=ℎ𝐿⁄ and β=𝛪ℎ𝛪𝑣⁄

Ih is the second moment of area of the beam.

Iv is the second moment of area of the columns.

RA and RE are the vertical reactions at supports A and E respectively.

HA and HE are the horizontal reactions at supports A and E respectively.

Strut-and-Tie Model

𝜈́=1−𝑓𝑐𝑘250 𝑤𝑡=0.5𝐿𝑡sin𝜃+𝑥cos𝜃 𝑥=𝑇1𝑡𝜎𝑐0 𝑇1=(0.5𝑃 𝑜𝑟 𝑃)𝑐𝑜𝑡𝜃 𝑐𝑜𝑡𝜃=(0.5𝐿−0.25𝐿𝑡)/(ℎ−0.5𝑥−𝑑′)

𝐶𝐸𝑑=0.5𝑃/𝑠𝑖𝑛𝜃 𝐶𝑅𝑑=0.6𝜈́𝑓𝑐𝑑min(𝑤𝑡,𝑤𝑏)𝑡

Bearing strength at top node = 𝜈́𝑓𝑐𝑑

Bearing strength at bottom node = 0.85 𝜈́𝑓𝑐𝑑

Figure: Axes of a Universal Beam or a Universal Columns section

Table: Universal Beam (UB) sections (properties)

Serial size

Mass per meter (kg/m)

Second moment of area

Elastic modulus

Plastic modulus

Wrapping constant

Torsional constant

Area

Iy

Iz

Wel,y

Wel,z

Wpl,y

Wpl,z

Iw

IT

A

cm4

cm4

cm3

cm3

cm3

cm3

dm6

cm4

cm2

838 X 292

226

339704

11360

7985

773

9155

1211

19.3

514

289

194

279175

9066

6641

620

7640

974

15.2

306

247

176

246021

7799

5893

535

6808

842

13

221

224

762 X 267

197

239957

8175

6234

610

7167

958

11 .3

404

251

173

205282

6850

5387

514

6198

807

9.39

267

220

147

168502

5455

4470

411

5156

647

7.4

1.59

187

134

1 50692

4788

4018

362

4644

570

6.46

119

171

686 X 254

170

170326

6630

4916

518

5631

811

7.42

308

217

152

150355

5784

4374

455

5001

710

6.42

220

194

140

136267

5183

3987

409

4558

638

5.72

169

178

125

117992

4383

3481

346

3994

542

4.8

116

159

610 X 305

238

209471

15837

6589

1017

7486

1574

14.5

785

303

179

153024

11408

4935

743

5548

1144

10.2

340

228

149

125876

9308

4111

611

4594

937

8.17

200

190

610 X 229

140

111777

4505

3622

391

4142

611

3.99

216

178

129

98610

3932

3221

343

3616

535

3.45

154

159

113

87318

3434

2874

301

3281

469

2.99

111

144

101

75780

291 5

2515

256

2881

400

2.52

77

129

L

L

R

RAA

R

REE

A

A

B

B

D

D

E

E

H

HAA

H

HEE

h

h

y

y

y

y

z

z

z

z

Page 12 of 12

Table: Universal Column (UC) sections (properties)

Serial size

Mass per meter (kg/m)

Second moment of inertia

Elastic modulus

Plastic modulus

Wrapping constant

Torsional constant

Area

Iy

Iz

Wel,y

Wel,z

Wpl,y

Wpl,z

Iw

IT

A

cm4

cm4

cm3

cm3

cm3

cm3

dm6

cm4

cm2

356 x 406

634

274845

98125

11582

4629

14235

7108

38.8

13720

808

551

226938

82671

9962

3951

12076

6058

31.1

9240

702

467

183003

67834

8383

3291

10003

5034

24.3

5809

595

393

146618

55367

6998

2721

8223

4154

18.9

3545

501

340

122543

46853

6031

2325

6999

3544

15.5

2343

433

287

99875

38677

5075

1939

5813

2949

12.3

1441

366

235

79085

30993

41 51

1570

4687

2383

9.54

812

299

356 x 368

202

66261

23688

3538

1264

3972

1919

7.16

558

257

177

57118

20529

3103

1102

3455

1671

6.09

381

226

153

48589

17553

2684

948

2965

1435

5.11

251

195

129

40246

14611

2264

793

2479

1199

4.18

153

164

305 x 305

283

78872

24635

4318

1529

5105

2342

6.35

2034

360

240

64203

20315

3643

1276

4247

1950

5.03

1271

306

198

50904

16299

2995

1037

3440

1581

3.88

734

252

158

38747

12569

2369

808

2681

1230

2.87

378

201

137

32814

10700

2048

692

2297

1052

2.39

249

174

118

27672

9059

1760

589

1958

895

1.98

161

150

97

22249

7308

1 445

479

1592

726

1.56

91.2

12 3