# Structures at Bath

## Question 17

📥  Beams, ST1

Question:  If x= L/3 what is the vertical reaction at support A?

Solution: To solve this  we  need to take moment about  a  point that we know  the  moment for. Point  B  is a pin  support for must have  zero moment.

1. So taking  moments about B we  have acting clockwise the moment  generated  by the vertical reaction A (Va * L).
2. This must be equal to the anticlockwise moments  generated  by  the  applied   loads, which are  equal to
• P*(2L/3) for the moment from the point  load
• (wL/2)*(L/4) for the uniform loading - the first  term in brackets is the total load the  second term is the lever arm to the centre of the load.

3. equating  clockwise and  anticlockwise and dividing  by L we get Va=(2P/3) +(wL/8)

## Revision questions coming up soon.

To help those  students who are  resisting  Structures 1A and Structures 2 in August/Sept I will be  uploading a question for each  course on a regular basis .

## Question 16

This week its something  a bit different! Understanding the causes of deterioration is just  as  important as  resolving  vectors.

The rail bridge over Westmoreland Road, (on the route of the U18 bus leaving  Oldfield Park  on the way to uni) Bath, England, is  showing  some signs of  distress. Ignoring the small  amount of vehicle damage to the beams there are 2 separate worrying  signs of  deterioration.

As knowledgeable  engineers you  should be able to identify both signs of  deterioration (in the beams only) and suggest  what  may have caused these. You can just about make out both from Google street view but its much  easier to spot if you actually see the bridge.

The signs of deterioration could be: shear cracks, flexural cracks, longitudinal cracks, spalling or random surface cracking.

The causes maybe anything from blocked expansion joints, to overloading, Alkali-silica reaction, carbonation, or poor concrete cover.

## Question 15

Which plausible load case will produce the maximum hogging moment in the structure?

Which plausible load case will produce the maximum sagging moment in the structure?

If you are struggling with this then have a look at the Solution, it  involves influence lines

# Something for my Bridge Engineering Students

Moment at B is Diagram  3, when the load is between B and D the moment at B is always zero
Moment at C is Diagram 4, when the load is at A, the moment C is hogging
Reaction at B is Diagram 2, when the load is at A the  reaction at B is greater than when the load is placed directly on B
Reaction at D is diagram 1, when the load is at A the reaction at D is downwards, as the load  move between B and D the reaction at D acts upwards with increasing magnitude.

Well done to the 62 correct submissions, below are the solutions  for those of  you ( not very many) who  got it wrong.

Solution:

Moment at B is Diagram  3, when the load is between B and D the moment at B is always zero

Moment at C is Diagram 4, when the load is at A, the moment C is hogging

Reaction at B is Diagram 2, when the load is at A the  reaction at B is greater than when the load is placed directly on B

Reaction at D is diagram 1, when the load is at A the reaction at D is downwards, as the load  move between B and D the reaction at D acts upwards with increasing magnitude.

# Something for all my Bridge Engineering students.

Pre-stressing a simply supported beam

For the simply supported pre-stressed beam shown above, calculate the maximum allowable  length (in meters) if the maximum tensile stresses due to the unfactored dead weight are limited to 1N/mm2.

Take the density of concrete to be 24kN/m3 and the centroidal  axis is at mid-height of the section.Please ignore any reliving effects or the action of live loads

hint1-prestress

Hopefully you got an  answer of 36.7m, which is less than the transportable limit of 40m. If you got anything  other than 36.7m please read the solution. week13 solution

## Question 12

For height  H of ? and L= ?m  the  correct answer is  16.7kN,  well done to  all  those who got the right  answer.  Hopefully  you  took  moments about the support  pins to find the vertical  reactions,  then  if you  take moments about the central pin you can find the  horizontal  force in the tie. If the arch had less than 3pins the  solution would be more complex!

## Question 11

This weeks question is submitted by our very own Tom Reynolds a PhD students studying the dynamic performance of Timber connections who has a healthy interest in slack-lines.

The violin player hears a  tearing  sound  and  quickly  sees that  the cable at  point A is  starting  to  fail!!  What   should be  do?

a) Steadily walk towards point A, to reduce the force in the line at A and get to safety.

b) Steadily walk towards point B, to reduce the force in the line at A and get to safety.

c)Stay very still so as not to induce any higher forces in the line at A, and signal to passers by to catch his violin'

Solution: Well it seems most of you went for option (c) - staying very still and throwing your expensive violin to a kind passer-by. This would be the most sensible thing to do. From a statics point of view Option (b) reduces the risk of failure as it will reduce the vertical reaction at A and hence the tension in the cable (remember the horizontal reaction at A and B must be identical from equilibrium).

Moving towards A is terrible idea!

## Christmas and New year holiday

Happy new year to everyone.  The weekly blog questions will start again ready for Semester 2.  In the mean time I hope you are all outside enjoying the snow. Why not try to build an ice sculpture.

For more inspiring ice structures check out this link to Hienz Isler's work.

## Question 10: Buro Happold & Emirates Air Line

Those kind folks at Buro Happold have written a difficult question for all us structural engineers to think about for the next 2 weeks. As its a bit harder than usual we have doubled the prize money, a £20 Amazon Voucher could be yours if you get it right!