Okay, this is definitely a simple question to start with.
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.
- So taking moments about B we have acting clockwise the moment generated by the vertical reaction A (Va * L).
- 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)
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 .
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.
The multispan bridge shown carries three different load types, Dead load (Red), Super-imposed dead load (Blue) and Live load (Yellow). The individual spans are identical in length and stiffness.
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
Well done to the 62 correct submissions, below are the solutions for those of you ( not very many) who got it wrong.
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
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
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!
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!
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.
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!
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