# Structures at Bath

## Question 24

The continuous  two span footbridge has a uniform EI  (100,000kNm^2) and carries a total load of 12kN/m over its entire length Following a recent flood both the left hand (A) and inner  support (B) sink by 25mm.  Using  any method determine the moment  over  support B.

HINT 1: Think about the relative  movement of each support.

## Question 23

3-D Bending moment and torsion diagrams are never easy, so practice makes perfect.

Having sketched the bending moment and torsion diagram for the structure above determine the moments and torsion acting on the base of the structure

## A quick question to make you think

You are sitting in a rowing boat in a small pond, you have an unopened  can of baked beans with you. If you throw the  can (which sinks)  into the pond what happens to the level of the water in the pond

www.amsterdamology.com

This question was  plagiarized from Prof Peter Goodhew, thanks Mark

SOLUTION:  The  water level goes down!  In the boat the mass of the can displaces its own  mass of  water (which is a lot of  water as the beans are  dense) when the  can of beans  sinks to the  bottom of the pond they  only  displace  their own  volume which is   small ( as they  are  dense) hence the water  level goes  down! Don't worry  a  beautiful illustration of the solution is coming  soon.

## Structures 2 Students: read this!

Dear All

I will be teaching  you AR20389 Structures 2 from week  4- 11. I will cover several methods of  structural  analysis that  you  need to use in later  courses  in order to  determine  moments and  forces developed in a  structure  due to the  actions put upon it.

All of my notes are available through Moodle,  this blog is a little added extra providing  you with a weekly question based on the work  covered in class its not  compulsory but it  will certainly  help you understand the subject in time for the exam in Jan 2015!

See you in class on tuesday.

mark

## Question 22

The beam below carries a load of triangular distribution with a maximum value of 3kN/m  at midspan. The  beam  is  made of Glulam with E=16GPa and has a second moment of  area Imajor =1×10^9 mm4

Determine the  deflection at mid-span due to the  applied  loads.

HINT (1) Determine the reactions due to applied loads (2) Determine the equation of the moment diagram. ( 3) use a unit load
(4) 1GPa is 1000N/mm2

Solution  coming  soon

## Question 21

For the statically determinate truss shown above determine the displacement at the point E (in mm).

Assume all members have the same EA= 10^5 kN and L=4m

You can solve this simple problem using virtual work. Firstly you must determine the forces in the truss (its determinate so just use statics once you have the reactions). Then find the forces in the truss  caused by a unit load placed at the posit where ewe want to know the deflection (E).

Multiple the two set of forces together for each member (L/EA) and sum! You should get a displacement at E of 2.1mm - SOLUTION

# For the statically determinate truss shown above determine the displacement at the point E (in mm).Assume all members have the same EA.You can solve this simple problem using virtual work. Firstly you must determine the forces in the truss (its determinate so just use statics once you have the reactions). Then find the forces in the truss  caused by a unit load placed at the posit where ewe want to know the deflection (E).Multiple the two set of forces together for each member (L/EA) and sum!

## Start of teaching 2013

Hi everyone,  its that  time of  year  again.   I will be   uploading  weekly  questions  for you all  to attempt.  These are not  assessed  but  they  will prepare you  for the  exam  in January.   If you are   stuck on a  certain question have look through  the  past 21  questions and the solutions !

Each  week  there  will be a  £5 prize   for the randomly selected  correct answer! This is open to anyone not just  Bath students.

Mark

## Question 20

Here is question for all of you retaking Structures 2 in September 2013

Imagine you are assessing the interesting cantilever beam arrangement shown below, you have conclude that the moment capacity of the supports is adequate but you are worried about the overall deflection at the very end of the structure. Both cantilever beams are of the same length and have the same EI value of 20 MN.m2.
By formulating a suitable compatibility equation and through using Flexibility analysis determine the deflection at C.
This is  a bit easier than a  standard  exam  question  but   would carry  about  50-60 % of the available marks.
Imagine you are assessing the interesting cantilever beam arrangement shown below, you have conclude that the moment capacity of the supports is adequate but you are worried about the overall deflection at the very end of the structure. Both cantilever beams are of the same length and have the same EI value of 20 MN.m2. - ( sorry  i cant get  wordpress to  make squared)
By formulating a suitable compatibility equation and through using Flexibility analysis determine the deflection at C.
This is  a bit easier than a  standard  exam  question  but   would carry  about  50-60 % of the available marks.
HINTS coming soon!
1. Firstly read through the solution for Q4! It  uses the same analysis technique.
2. Draw yourself a primary  structure and a Unit load structure

## Question 19

Judging from last weeks performance quite a few of you have forgotten  how to draw BMD. So the next few questions will focus on this  issue.

The question focusses on  a 3 span  bridge with a  drop-in span in the middle similar to the Ness Bridge in Inverness Scotland, check out the Happy pontist blog: a  great  resource from  civil engineering  students.

HINT. The  trick  with  such  'drop-in' structures is that the double pin in the middle isolates the effects of load ( moment) from  either side. That is to say that a load on the  first span  cannot produce any moment on the middle or  third span.UPDATE 15/7/13. Judging  from the number of incorrect answers this  question  has  received I will be leaving it  up  for  a couple of  days  more.

If you  draw the deflected shape for the case where there load is at any point between the first  support and the adjacent pin, you  should see that  the middle span(between pins ) is always straight just  rotated slightly)

Try the question again and attempt to draw the deflected shapes.

SOLUTION: 17/6/13. A,C,D are the INCORRECT BMDs (this is what  you were asked to submit)  the  rest of them (B,E and F) are the correct BMD for the structure.

## Question 18

📥  Beams, ST1

Here is a question from  structures 2 but i'm sure  first years will  get it  right.

Question:  Which  BMD is the  correct for the cantilever beam  shown?

Solution: Lets  start from the point  where the load is  applied. It might help  if you  sketch the problem and mark a  line across the structure showing the  direction of the  applied load

1. The  bending moment will increases  linearly when we move away from the load ( we are moving  left) - all  diagrams  show  this!
2. As we move  down the vertical member on the  left  hand-side the  moment is constant as we are always the same perpendicular distance  from  the direction of the load.
• Note that at the corner the BMD are both on the  outside as there is tension on this face.
3. As we move along the bottom beam ( left to midpoint) we get closer and closer to the  direction of the applied load so the  moment  decreases linearly
4. As we  go past the  midpoint on the bottom beam  the bottom beam we get further  away  form the direction of the applied load and hence the moment increases linearly-only diagrams C & D show this.
5. If  we  move  up  the  vertical member on the right hand side we  stay a constant perpendicular distance  form the direction of load and so the moment is constant - the moment is on the  inside of the member  as this is  the face where  we have  tension. – Only diagram D shows this.

Lastly as we move along  the  top beam (right to left)  the moment  must  become less negative and reach  zero at the  point where we are inline  with the direction of load, when  we  have travelled  past  this  towards the  support the moment the moment increases and becomes  positive indicating a region of hogging bending ( tension on top face) near the  support