Structures at Bath

Keeping the concepts fresh

Posts By: Mark Evernden

Question 9

📥  Uncategorized

The top and bottom chord of the long truss shown below are CHS sections, and each has I = 31x106 mm4 and A = 6300 mm2. Take Esteel = 200 GPa. All members have the same length of 1m.  Determine the approximate deflection at  mid-span.
week9The correct answer is 26mm. The truss can be approximated to a beam. The second moment of Area of the 'beam' can be determined using parallel axis theorem allowing standard beam deflection equations applied for an approximate answer.

 

Question 8

📥  Frames


Correct  SFD is D:  Check  out http://expeditionworkshed.org/applets/2D_frames/sketch_10/sketch_10.html for a great pushmepullme model of the problem.

week8-easy

Thanks to  Al  form  supplying  the answer

The answer is: D

Since the load is applied at an angle, there two components of that load: Horizontal to the column (inducing the vertical reaction at the roller support) and perpendicular to the column which causes the shear in the upper part of the column.

Question 7

📥  Cables

Would you like a quick revision of simple hanging cables? CLICK HERE

If the cable has a diameter of 24mm what is the maximum stress in the cable?

week 7

The correct answer is approx 676N/mm2, if you  got it wrong please check out the full SOLUTION

 

Question 6

📥  Beams

For the structure shown below calculate the position of the roller support from the free end of the beam (C) such that the moment at the fixed end (A) is zero kNm.

week6


[Solution x=3.33m]

If  you didnt get it right or were unsure of the BMD or deflected shape check out this SOLUTION

Question 5

📥  Design

After the maths of last week's question, here is something to make your brain work in a slightly different way!

UPDATE: Its about real world design and the implications of inaccuracies in construction.

A person weighing 600N sits on a three-legged stool.  For what basic force should each leg be designed? There is no catch to this problem - the stool is to be symmetrical, the person sits in the center of the seat.  The answer is of course  200N

The same person now sits on a square  stool with four legs, one at each corner and again the stool and the loading are symmetrical. For what force should each leg of the stool be designed?

You can assume the floor is flat and rigid! Once you have decided how much load each leg should be designed for, please answer the question below.

Which type of stool uses the least  amount of material in the design of each leg?

Voting  is now closed!

Well done to the 62 people that entered the quiz. If you consider that the length of each leg maybe very slightly different, then the 3 legged stool is by far the best design requiring 50% of the material in the legs than the 4 legged stool.

If you didn’t get this answer please read through the SOLUTION.

Mark

 

Question 4

📥  Uncategorized

Something a bit harder this week to keep you all on your toes!

What diameter of steel cable is required such that the mid-span deflection of the timber beam is only 50% of the mid-span deflection of the beam without the cable?

week4

Click the link below for the solution-->
MPS-6E4-02_4201_001

Question 3

📥  Frames

week3
Match each Shear Force Diagram (SFD- red)  with a Bending Moment Diagram (BMD-blue).
Hint: BMDs are drawn on the tension side of the deflected shape.

Match each Shear Force Diagram (SFD- red)  with a Bending Moment Diagram (BMD-blue).

Hint: BMDs are drawn on the tension side of the deflected shape.

Solution

SFD:BMD (A:C)

SFD:BMD (B:D)

SFD:BMD (C:A)

SFD:BMD (D:B)

 

Question 2

📥  Frames

No  calculations this week! Which BMD matches the load-case for the structure shown below ?

2FrameBMDCQ5

Choose  from the  following

  1. 2FrameBMDCQ5C
  2. 2FrameBMDCQ5B
  3. 2FrameBMDCQ5D
  4. 2FrameBMDCQ5A

What a week over 60 entries! Unfortunately only 50% of them correct ( BMD:4).

Quick Explanation: As the right hand support is a horizontal roller there is no horizontal reaction at this point – therefore there is no moment generated in the right hand column.
As there is no horizontal reaction at the right hand support, all of the horizontal applied force is taken by the left hand horizontal reaction, hence the left hand column behaves like a cantilever.

Question 1

📥  Frames, Numbers

Calculate the BM at the top right corner when x = 3.9m and P = 4.3kN.
Write your answer to one decimal place and in units of kNm

1SimpleBeamNumbersBQ5

Congratulations to Barrie Dams you've won some chocolates!

Tim Ibell, Antony Darby, Charlie Banthorpe, Natasha Watson and Ze Wen also got it right!

The answer is  8.4kNm,  click  on  the link  below for  a worked   solution.

MPS-6E2-02_0371_001


Trial Question 1

📥  Uncategorized

Okay here goes,  our first trial question.  Get your pens ready ...GO

Picture2

The largest BM felt by this Virendeel truss is approximately:
A. 10 kNm in BE
B. 5 kNm in AD
C. 40 kNm in BC
D. 20 kNm in EF

Submit your answers to  structures@bath.ac.uk

A solution will be posted early next week. Good luck!

Here is my worked solution