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Homework answers / question archive /   QUESTION 1 (Mark 8/15)   Consider the structure and the corresponding cross-section shown below

  QUESTION 1 (Mark 8/15)   Consider the structure and the corresponding cross-section shown below

Math

 

QUESTION 1 (Mark 8/15)

 

Consider the structure and the corresponding cross-section shown below. Use the stiffness method to calculate:

  1. all nodal displacements undergone by the structure;
  2. the reactions at nodes A, B and C. Provide a clear and detailed free body diagram of the entire structure to illustrate your answer; 
  3. the local end actions for member 2 (which connects nodes B and C). Provide a clear and detailed free body diagram of member 2 to illustrate your answer; and
  4. draw the Axial Force Diagram (AFD), Shear Force Diagram (SFD) and the Bending Moment Diagram (BMD) for the structure analysed and provide significant values on the diagram.

 

In your solution select the type of element which is most appropriate for the structure considered and briefly explain the reason for your choice. 

Provide all details and steps performed in your solution. Also, clearly state the sign convention adopted in your calculations and make sure to use the location vectors illustrated below. Assume E to be 200 GPa. 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

A

 

C

 

6

 

kN/m

 

6

 

m

 

B

 

8

 

m

 

location vector

 

2

 

8

 

m

 

1

 

locati

on vector

 

 

 

 

            200 x 12

 100 x 12

 

 

 

            Cross-section

            (all dimensions are in mm)

 

 

 

QUESTION 2 (Mark 7/15) 

 

Consider the structure and the corresponding cross-section shown below. Use the moment distribution method to calculate: (i) the amount of sway undergone at node C;

  1. the reactions at nodes A and D. Provide a clear and detailed free-body diagram of the entire structure to illustrate your answer; and
  2. draw the Axial Force Diagram (AFD), Shear Force Diagram (SFD), Bending

Moment Diagram (BMD) and provide significant values on the diagram

 

Provide all steps and details of your solution. Assume E to be 200 GPa.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A

 

C

 

w

 

 

=

5

 

kN/m

 

 m

10

 

5

 

m

 

D

 

B

 

 

20

kN

 

2

 

m

 

 

 

 

Cross-section (all dimensions are in mm):

 

 

            15 130

 

 

            130

 

 

 

NOTE: 1. Dashed lines are dimension lines.

    1. Please submit the print-out or hand-written assignment only.
    2. Please keep the electronic copy or a scanned copy (if it is written by hand) to yourself.  

 

 

Additional Information

  

 M

 

 

 

 

L

 

 

M

FE.A

 

A

 

B

 

     w   FE.B

 

M FE.A wL2 /12 M FE.B wL2 /12

 

 

 

 

 

L

 

    

w

 

 

M

FE.B

 

 

M

FE.A

 

A

 

B

 

20

/

2

FE.A

wL

M

 

 

30

/

2

FE.B

wL

M

 

 

 

 

 

 

 

L

 

    

w

 

A

 

B

 

 

 

 

M

FE*.A

 

8

/

2

.A

*

FE

wL

M

 

 

 

 

 

 

L

 

    

w

 

A

 

B

 

 

 

 

M

FE*.A

 

 

M FE*.A wL2 /15

 

 

 

 

 

 

 

a

 

 

P

 

b

 

L

 

 

M

FE.B

 

 

M

FE.A

 

A

 

B

 

2

2

FE.A

/

L

Pab

M

 

 

2

2

FE.B

/

L

b

Pa

M

 

 

 M

 

 

 

 

 

 

 

L

 

FE.A

 

A

 

B

 

'

 

 MFE.B

 

M FE.A 6EI'/L2 M FE.B 6EI'/L2

 

 

 

a

 

 

P

 

b

 

L

 

 

M

FE*.A

 

A

 

B

 

 

 

 

 

 

 

2

2

2

.A

*

FE

/

2

/

L

P

b

a

ab

M

 

 

 

 

 

 

'

 

 

 

 

 

 

 

L

 

M

FE*.A

 

 

A

 

B

 

2

.A

*

FE

/

3

L

EI

M

'

 

 

 

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