past exams matrix and solns 1516

8/18/2019 Past Exams Matrix and Solns 1516

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Dr D R Gordon, Matrix Analysis, Exam Solutions, 2015/16

Dr D R Gordon, ED&A4 Trimester 1 Session 2015-16 Page 1

ENGINEERING DESIGN

& ANALYSIS 4

Past Exam Questions & Solutions

Jan’08 – Jan’15

MATRIX

ANALYSIS


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JANUARY 2015 (14-15)

Q.1 The frame shown in Figure Q.1 has a sliding pin joint support at D and E,

while at C the structure is fully fixed. Member BC carries a uniformly

distributed load of 12kN/m along it’s length. Member BD has a discrete mid

span horizontal force of 20kN as shown. The non-structural cantilever

overhang AB carries a discrete load of 15kN and the sliding support at Eexperiences a vertical load of 70kN. All members each have the same flexural

rigidity EI of 104 kNm2.

(i) Using the Displacement (Stiffness) method of matrix analysis and considering

flexural deformation only, determine the stiffness matrix for the structure.

[6]

(ii) Determine the load vector for the applied loading.

[6]

(iii)

Determine the displacement of B and the reactions at pistons D and E.[13]

Figure Q.1

6 m

20 kN

12kN/m

3 m

15kN

A

BC

D

E

3 m1.1m

70kN

Cantilever

beam AB

Sliding support with

pin-jointed connection

,


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JANUARY 2014 (13-14)

Q.1 The frame ABCDEF shown in Figure Q.1 is rigidly fixed at A and pin joint

supported at D. Horizontal motion is prevented by means of a tie bar FB

which is pin jointed at both ends and attaches to the structure at B. The

structural members AB, BC and BE are continuous and rigidly connected at B.

The relative flexural rigidities are as indicated where EI is 10MNm 2.

Considering flexural deformation only and using the Displacement (Stiffness)

method of matrix analysis and using DATASHEET Q.1, determine:

(a) The stiffness matrix [K] for the structure.

[6]

(b) The loading vector [P].

[4]

(c)

The displacements at B and C[5]

(d) The load acting in the tie bar FB.

[10]

A

B C

D

E

F

6 kN/m

15kN

20kN 2EI

3EI

EI

10m

5m

5m

2m

2.5m

Figure Q.1


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DECEMBER 2012 (12-13)

Q.1 The frame structure ABCDE shown in Figure Q.1 is rigidly fixed at A, D and

E. Members BE and CD carry a uniform distributed load of 2kN/m.

Member BC has a 20kN load acting horizontally at mid-span. The relative

flexural rigidities of each member are as shown in Figure Q.1, where EI is

10MNm2.

Considering flexural deformations only, and making use of the supplied

DATASHEET Q.1, determine:

i) the stiffness matrix [K] for the structure;

[5]

ii) the loading vector [P] for the structure;

[5]

iii) the displacements at B and C;

[5]

iv)

all reactions acting at D;[5]

v) the Bending Moment Diagram (BMD) for member CD.

[5]

5 m

10

2kN/

2kN/m

4EI

2EI

EI

EI

20kN

A

B

C D

E

5 m

2.5

5 m

Figure Q.1


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DEC 2011 (11-12, NEW TRIMESTER SYSTEM)

Q.1 The frame structure ABCDEF shown in Figure Q.1 is pin supported at A, fully

fixed at C and F and has a pin joint support at E. Member AB carries a discrete

force of 10kN at the position shown, member CD carries a uniformly

distributed load of 6kN/m and a discrete force of 24kN is applied to DE at

mid-span. The members each have their relative flexural rigidities asindicated, where EI is 10MNm2. Determine:

(a) the stiffness matrix [K] for the structure using the Displacement

(Stiffness) method of matrix analysis and considering flexural

deformation only;

[6]

ii) the load vector [P] for the applied loading;

[6]

iii) the displacements at D and E;

[4]

iv) the bending moment MDE, the reactions at E, and sketch the bending

moment diagram for portion DE.

[9]

Note: Use may be made of DATASHEET Q.1

D

A B

C E

4m

6m10m

4m

4m

10 kN

6 kN/m

EI

2EI2EI

2EI

Figure Q.1

F

EI

24kN

3

3


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DEC 2010 (10-11, NEW TRIMESTER SYSTEM)

Q.1 The frame ABCDE shown in Fig.Q.1 is rigidly supported at A, simply

supported at D, and carries uniformly distributed loading of 12kN/m and

6kN/m along members AB and BD respectively. A horizontal discrete force of

16kN is also applied at point C on member BD and a vertical discrete force of

10kN acts at E.The frame members have their relative flexural rigidities as shown, where EI

is 104 kNm2.

(a) Using the Displacement (Stiffness) method of matrix analysis and

considering flexural deformation only, determine the stiffness matrix

[K] for the structure.

[6]

(b) Determine the load vector [P] for the applied loading.

[6]

(c) Determine the displacements at B and the reaction at support D.

[13]


12kN/m

6kN/m

16kN

10kN

Figure Q.1


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JAN 2010 (9-10)

Q.1 The viaduct structure ABCDEF shown in Figure Q.1 is pin supported at A,

fully fixed at E and F and has a pin joint support at D. Member AB carries a

discrete force of 30kN at the position shown, member BC carries a uniformly

distributed load of 6kN/m, and a discrete force of 40kN is applied to CD at

mid-span. The members each have their relative flexural rigidities asindicated, where EI is 10MNm2. Determine:

i) the stiffness matrix [K] for the structure using the Displacement


deformation only;

[6]

ii) the load vector [P] for the applied loading;

[5]

iii) the displacements at B and C;

[5]

iv) the bending moments MBA, MBC, MCB, and MCD and sketch the

bending moment diagram for the beam portion BC.

[9]


DAB C

E

2m

6m10m8m

6m

30 kN

6 kN/m

2EI

EI2EIEI

Figure Q.1

F

EI

40kN

3

3

4m


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JANUARY 2009 (08/09)

Q.1 The frame structure ABCDE shown in Figure Q.1 represents an idealized

crane geometry and is fully fixed at A and E and has a pin joint support at D.

Member CD carries a uniformly distributed load of 15kN/m and a discrete

force of 30kN is applied to BC at the position shown. The members each havetheir relative flexural rigidities as indicated, where EI is 10MNm2. Determine:

(i) The stiffness matrix [K] for the structure using the Displacement


deformation only;

[6]

(ii) The load vector [P] for the applied loading; [4]

(iii) The displacements at B and C; [5]

(iv) The bending moments MBC MCB and MCD and the vertical

reaction at C. [10]


D

A

B C

E

4m

6m6m

4m

4m

30 kN

15 kN/m

EI

2EI2EI

EI

Figure Q.1


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JANUARY 2008 (07/08)

Q.1 The frame structure ABCD shown in Figure Q.1 has a pin joint support at A,

fully fixed at C and has a pin-jointed slider at D. Members AB and BC carry a

uniformly distributed load of 10kN/m and discrete forces of 20kN are each

applied at mid-span respectively. In addition a 50kN horizontal force is

applied to the pin-jointed slider at D. The members each have their relativeflexural rigidities as shown, where EI is 10MNm2. Determine:

(i) the stiffness matrix [K] for the structure, using the Displacement


deformation only;

[8]

(ii) the load vector [P] for the applied loading;

[6](iii) the displacements at B, and D and the bending moment MBD at B

on member BD;[5]

(iv) the magnitude and direction of the reaction force at the piston at D.

[6]


10kN/m

20kN

A

B

C

2EI

2EI

6m

20kN

EI

D

50kN

4m

4m

Figure Q.1


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JAN 2015 MATRIX SOLUTION:


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JAN 2014


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DEC 2012


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DEC 2011


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DEC 2010


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JAN 2010


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JAN 2009


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JAN 2008


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past exams matrix and solns 1516

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