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.
CLICK to submit your answer
HINT 1: Think about the relative movement of each support.
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
Submit your answers here <CLICK> remember to state which axis the moments are acting about!
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
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.
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.
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
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
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.
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. - ( 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!
- Firstly read through the solution for Q4! It uses the same analysis technique.
- Draw yourself a primary structure and a Unit load structure
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.
Please identify the INCORRECT BMDs
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.
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
- The bending moment will increases linearly when we move away from the load ( we are moving left) - all diagrams show this!
- 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.
- 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
- 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.
- 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