Quiz 2 2017, questions and answers PDF

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Examples of in class quizzes 2's for Structural Analysis...

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UNIVERSITY OF TECHNOLOGY, SYDNEY School of Civil and Environmental Engineering

48349 Structural Analysis

Test 2

Student Name:

S________________________________ OLUTION

Student number:

________________________________

Mark

/ 10

Marker Name:

________________________________

Marker number:

________________________________

Notes:

Time allowed 45 minutes.

Write your solution and answers in the space provided in question sheet Write formulas used and short comments to explain how you arrived at your answers. Correct numerical answers alone will not attract the full mark.

483 48349 49 St Structur ructur ructural al Analy Analysis sis

Te Test st 2

Aut Autumn umn 201 2018 8

Page | 3

483 48349 49 St Structur ructur ructural al Analy Analysis sis

Te Test st 2

A.2

Aut Autumn umn 201 2018 8

Integration Tables*

Value of Integral:

(Table Value)

Value of Integral:

(Table Value)

* Based on Table 3.1 in Beton-Kalendar 1974. ref [13] Page | 5

All members displace rigidely

UNIVERSITY OF TECHNOLOGY, SYDNEY Faculty of Engineering

48349 Structural Analysis

Test 2

Student Name:

____________Solution____________________

Student number:

________________________________

Notes:

Time allowed 45 minutes + 5 minutes Reading time. The Test is a closed book exam. Write your solution and answers in the space provided in question sheet Write formulas used and short comments to explain how you arrived at your answers. Correct numerical answers alone will not attract the full mark. Please do not use red or green colour pen. All question sheets must be returned with the solution. Failure to submit the question sheet may lead to loss of marks.

48349 Structural Analysis Question 1

Test 2

Autumn 2017

(7 Marks)

Determine the horizontal displacement at point A for each of the actions of force P and change in temperature affecting AB only.

P= 20 kN 30

O

A 10 O EA = 4×104 kN EI = 104 kNm2 α = 10-5/◦ d =400mm

d

B

D 3m

E

C

8m

2m

4m

Hint: When the structure was analysed under the action of a concentrated unit force F* acting on its own at point A, the results shown below were obtained. You may use this information in your computations. F*=1 3 16 0

1

15 16

3 4

1 (T)

N*

(T)

15 (C) 16

5 4

1.5

0 M*

0

Page

1

48349 Structural Analysis

Test 2

Autumn 2017

Solution Apply the Principle of Virtual Work to compute the required displacement at A. Take the force system given in the hint as the virtual force system because F* acts in at point A in the direction of the required displacement. Solution steps: 1)

Analyse the system under the load P to determine axial force and moment diagrams and the corrsponding strain and curvature diagrams.

2)

Determine the strain and curvature that result from tempearture change in AB.

3)

Evaluate the Virtual Work equation leading to the horizontal displacement at A.

Step 1: Load P only and considering Equilibrium of FBD-1 and FBD2 shown below:

P= 20 kN Dx = 0

A

D

B

Dy = 0 Ay = ?

3m 2m

FBD-1 C 8m

FBD-2 E

Cx = 0 Cy = ?

4m

Ex = 0 Ey = 0

Reactions In FBD1: BC is pin-ended with no internal loads applied  Cx=0 Considering Fx=0 in FBD-1 leads to Dx=0

Transferring Dx=0 to FBD2 then Fx=0 leads to Ex=0

In FBD2: MD=0 leads to 4Ey =0 and Ey=0

Fy=0 leads to Dy=0 which is transferred to FBD1

In FBD1: MB=0: 8Ay  2(20)=0 leads to Ay= 5 kN 

Fy=0: Cy  20  5 = 0 leads to Cy = 25 kN  20 kN

A

B D 5 kN

C

0

0 E

25 kN

0

Page

2

48349 Structural Analysis

Test 2

Autumn 2017

Internal Actions

25 kN

0

N

0 (C)

40 kNm

0 0

M

Real displacement system – when only force P is applied 0 0

P

25 4×104

40 104

0 P

0

Page

3

48349 Structural Analysis

Test 2

Autumn 2017

Step 2: Strain and curvature resulting from tempearture change in AB

30°

TG=+20

Tu=10°





(30  ( 10 ))  10 2   Tu  10 10 5 10 4 Tu 

(30  ( 10 ))  20 2  Tu   20  10 5    0.001 d   0.4  2   2      TG 

10°

TG=-20°

10-4

0.001 0

e

T

0 0

0

0

T

0

Step 3: Evaluate the Virtual Work equation leading to the horizontal displacement at A Evaluate the equation for both P and T simultaneously

Page

4

48349 Structural Analysis Question 2

Test 2

Autumn 2017

(3 Marks)

For structure and loading shown below, determine qualitatively and draw support reactions, deformed shape and all internal action diagrams (N, V, M). 

Use arrows to show the direction of non-zero reactions. Do not draw arrows for zero reactions or write a zero next to the arrow.



Draw deformed shapes clearly and indicate any members that remain straight after deformations. Identify points of inflection by writing “IP” next to such points if they exist.



Draw bending moments on the tension side, use “T”/“C” to indicate tension / compression and use “+” / “-“ for the sign of shear forces.

P

Given: EA=∞

Structure & Loading

(a) Support Reactions

Straight C

T

No IP’s

(b) Deformed shape

0

0

0

0

C

(c) Axial Force Diagram

0

0

+

+

(d) Shear Force Diagram

(e) Bending Moment Diagram

Page

5

48349 Structural Analysis

Test 2

A.2

Autumn 2017

Integration Tables*

Value of Integral:

(Table Value)

Value of Integral:

(Table Value)

* Based on Table 3.1 in Beton-Kalendar 1974. ref [13] Page

6

Instantaneous centre of rotation of BCD

Rigid displacement

Rigid displacement Instantaneous centre of rotation of BCD Rigid displacement

Rigid displacement

UNIVERSITY OF TECHNOLOGY, SYDNEY Faculty of Engineering

48349 St r u c tu r al An al aly ys i s

Test 2 Group A

Student Name:

_________Solution_______________________

Student number:

________________________________

Notes:

Time allowed: 30 minute minutes s. The Test is a closed book exam. Write your solution and answers in the space provided in question sheet Write formulas used and short comments to explain how you arrived at your answers. Correct numerical answers alone will not attract the full mark.. Please do not use red or green colour pen. All que ques s ti on s he hee ets m ust be rre eturne turned d w it h t he ssolution. olution. Failure to s ubm ubmit it t he que questi sti on s he hee et m ay l ead to l oss of m arks.

Test 2 – Group A

48349 Structural Analysis

3m

Question 1 (10 marks) Determine the vertical displacement at point A for the combined actions of the applied force P, the support settlement at D and the change in temperature, which affects member BC only.

6m +15 O

B

A

C

−5O 3m

Given: EA = 105 kN

Autumn 2016

600 mm α = 10−5 /OC

P = 100 kN D

EI = 2 x 106 kNm2

−5 O

δ = 4 mm

α = 10 / C

Whe hen n tthe he fforce orce P i s applie pplied d on i ts ow n, tthe he s upport r eactions, a axia xia xiall f orce di dia agra gram ma and nd mome moment nt di agra gram m w oul d be a as s de depicte picte picted d be below low

Reaction A

C Cx = 0

B

P = 100 kN

Cy= 50 kN D Dy= 150 kN

300 kNm 0

0

C

0

C

A

150 kN

A

0 N

M

D

A

0

D

300 6 2×10

C

0

B

A 150 C 5 10 D

C

B

C

B 0

εP

ΦP

D

Page

1

Test 2 – Group A

48349 Structural Analysis

Autumn 2016

Temperature effects ∆TU=5°

o

+15 C A

+15

B

O

C +

=

−5O o

-5 C

600 mm D

+∆TG=10°

1 (15 + (−5) ) = 5 2 ε U = α ×T U = 5 × 10 −5

∆TU =

α = 10−5 /OC

1 (15 − (− 5) ) = 10 2 ε G = α ×T G = 10− 5 × 10 = 10− 4

∆TG =

ΦT =

εG 1   D 2 

=

10 −4 = 3.333 × 10−4 0.6     2   -4

-5

3.3333 × 10 Φ

5×10 A

A

e

0 B

0 B

C 0

C 0

εT

ΦT

D

D

Vi Virrt u al Fo r ce Sy s t em B

A

C

F* = 1

Cx* = 0

Cy*= 0.5 D

.

Dy*= 1.5 3 A

0

B

C

0

A C 1.5

0 n

D

C

B m D

Page

2

48349 Structural Analysis

Test 2 – Group A

Autumn 2016

P.V.W ∗ ∗ Wext = Wint

Rs∗δ s + F ∗ ∆ = ∫ nε dx + mΦdx

c c n ε

m +

ΦP

+

ΦT

1  300   150  1.5 × ( −0.004) + 1× ∆ A = (3)m (1.5)  5  + (3 + 6)m (3)   3  2 × 10 6   10      R ∗Dy× δ Dy LBD × jk

LABC ×

1 jk 3

1 + (6) m (3)(3.3333 × 10 −4 ) 2   1 LBC× jk 2

∆ A = 0.00678 + 0.00135 + 0.002997 + 0.006 ∆ A = 0.01709 m(↓ )

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