Great work with 99.9% another 0.1% would be perfect If you show the truck or tandem moving inside the greatest area to decide the maximum value for height*point load. (Not shown at all but just one or two example initially)
Quick question, what if the bridge consists of four steel girders like this example, but there it no splice (hinge reaction) and the interior support is a concrete pier bolted to the girders using bearing plates? Would the concrete pier be considered a fix support? If so, how would this change the influence lines?
Generally, that would be considered a pin support. If the connection is actually made so as to behave as a fixed support, then we would end up with two independent beams, one to the left of the support and one to the right of it. If we view the connection as a pin support, without the splice, the beam becomes statically indeterminate. Its influence line would no longer consists of straight lines, rather it becomes nonlinear (curve) in shape.
Thank you for this lecture. Pls send video on how to go about this one also. I hope it will add on to know the difference between the two : ( splice) and pin connection. God bless you
How to find the values of these lane loads? Do I need to memorize it or will it be given?If you've a lecture about this lane load plz provide the link this Will be very helpfull
The lane load values are given in the governing design specifications for the target geographic location. In the United States, the governing specifications for highway (bridge) design are provided by the American Association of State Highway and Transportation Officials (AASHTO). The LRFD Bridge Design Specifications (published by AASHTO) provide the load details. You can download the table of contents of the specifications here: store.transportation.org/Common/DownloadContentFiles?id=2049 As a professional engineer, you need to have access to relevant design codes and specifications. As a student, you either have access to the needed specifications or the load values are provided to you, depending on the course you are taking. In a structural analysis course, most often, the load values are provided. In a design course where getting accustomed to the use of code and specifications is a course objective, you will learn how to navigate the specifications in search of relevant information.
Thanks for the feedback. The bridge model was created using SketchUP and rendered and animated using Lumion. The lecture presentation was prepared and animated using Adobe Illustrator. The avatar was made and animated using Reallusion software suite. The various pieces of the presentation were put together for producing the final video using Camtasia Studio.
25:24 why did you draw bending moment at B, while we are looking for bending moment at D ? Also, what reason did you use to calculate bending moment by multiplying only 1 external force (unit force) on FBD by distance (3 m) neglecting contribution of 2 other external forces shown on particular FBD ? I think that part is unclear. Thanks.
@25:24 we are not drawing the bending moment diagram. Rather, we are drawing the influence line for the bending moment at B. That explains why we are using a unit load. An influence line is always drawn using a unit load. @24:24, we assert that the beam's maximum negative moment could occur at point E or at point B. To decide which point controls the design, we must draw the moment influence line for each point and compare the two diagrams. The moment influence line for point E is shown @24:53. The moment influence line for point B is shown @26.04. Since a larger negative area is associated with the latter influence line, we conclude that the moment reaches its max negative value at point B. Now we place all the applied loads on the governing influence line (point B) to determine the max negative bending moment value at that point.
Good day Dr. Structure! Could you please help me understand the following? (1) At 21:00 why did we not consider vertical reaction Dy due to shear splice (internal hinge) as done at 21:32? (2) In Influence Lines, the vertical distance = value of reaction (or) shear (or) moment. So, qualitatively, what does the area under the influence line represent? (3) Why is the lane load categorized as transient load? Doesn't this value not change?
1) @21:00 the shear force at the hinge is not shown, because it is zero. We could have (should have) shown the force vector and then derived its zero value from the equilibrium equations. 2) The height of the influence line represents reaction and shear values, but not moment values. When dealing with moment, the influence line gives us the load pattern that causes max/min moment values at a given point, but we then need to analyze the beam under that pattern to actually determine the values. There is no meaningful qualitative interpretation for the area under the diagram. 3) By definition, Lane Load is attributed to a series of vehicular loads that move in close proximity of each other in such a manner that their weights can be treated/viewed as being uniformly distributed, more or less like a train on a track. Since the load is that of hypothetical vehicles, it is not a permanent fixture on the bridge, it falls under the transient label.
@@DrStructure Wow! For (2) you've clarified perfectly. I understand completely. For (3) I mistook the definition. My apologies. Its interesting to note that US aashto determines gaps between trucks/cars (say 10m gap) for designing. Canada on the other hand assumes a packed traffic jam for designing (no gap. For (1), I am getting 4 equations for Sum Fy=0, Sum Mx=0: Ay + By + Dy -1= 0, (Ma eqn)= 4.5 - 9By - 12Dy = 0 (Mb eqn)= 9Ay - 4.5 - 3Dy = 0 (Md eqn)= 12Ay + 3By - 7.5 = 0 I thought shear splice generates/resists no moment therefore no Md marked. Solving the above system of equations (either by hand or by an online tool (such as Wolframalpha or symbolab)) shows that Ay, By, Dy will be in terms of another unknown. Please help me if I've generated the system of equations correctly.
On Question 1, we cannot solve the problem (determine all the unknowns) by just examining segment AD. We need to bring segment DC into the formulation before we can calculate all the unknowns. Given that the beam has an internal hinge at D, we need to write the equilibrium equations for both AD and DC. Starting with segment DC (not shown in the video), we can see that the free-body diagram for the segment consists of two forces, the shear force at D and the reaction force at C. Let’s label these forces Dy and Cy. The equilibrium equations for the segment can be written as: SUM of Fy: Dy + Cy = 0 SUM of Moments (about C): 12 Dy = 0 Solving these equations for the unknowns, we get Dy = 0 and Cy = 0. This means that the shear force at the hinge is zero. And more generally, the segment carries no internal force. So now if we examine segment AD, knowing that there is no shear force at D, we arrive at the free-body diagram and the results shown in the video.
@@DrStructure Ohh So that's what I missed out. I was aware that internal hinge(s) help "convert" statistically indeterminate structures into determinate ones, I just thought we could analyze either section. Thank you for the detailed explanation Prof! You're amazing!
Correct me If I'm wrong. Are these four girders laterally supported (support in-between girders) called CROSS_BEAMS or DIAPHRAGMS? Are these girders sitting on PIER CAPS?
It depends on the location of the girders relative to the slab. Here, we are assuming that the slab has an overhang at either end. That extra weight of concrete makes the two exterior girders carry the same amount of load as the interior girders. If the exterior girders had been placed at the edge of the slab, then yes, they would have been subjected to less loads than the other girders.
@@DrStructure I hope you don't get me wrong, I like your work, but the over hang doesn't seems to me to be like half of internal span, plus you must've mentioned the barriers weight on both sides. Thanks for your great work, many students and even graduated engineers are getting benefit from your channel.
@@totticapitano1 yes you are right as the loads from footpath and crash barriars is also to be considered on external girders and also the loads due to cross girder on all girders is to considered.
@@Spatidar1994 For brevity, simplicity, and clarity of the presentation, for illustrating the essence of the lecture (influence line usage), several load sources have been excluded from this analysis.
There is no fixed support here, there are only pin and roller supports. Regardless, the type of supports used in a structure is always a design decision. In this case, the engineer has made those decisions already, we are simply using the given information to analyze the bridge.
Please elaborate why you are making the distinction here? In this lecture, we are discussing influence lines; we are not discussing the design of the structural members. Whether the member is a standard beam or a customized deeper beam (i.e., a girder) has no bearing in our analysis.
In the case of the bridge we are considering, that would be a distinction with no difference. On the other hand, in the case of a floor girder where the girder is not a continuous beam, rather it is a series of simply supported beams, that distinction becomes relevant.
@@DrStructure I will take this chance to ask another question, In a given beam, supports, and axle loads , How can we know the point on the beam where the maximum shear or moment will occur?
Could not get it yet from anywhere on youtube!! Influence line does not make any sense to me at all,, why we need it? What is the difference between this and the ordinary or usual way of calculating loads on beams???? If i have a beam with point load then its easy to get the reaction forces at supports whatever is the location of this load,, why there is a topic called influence line 😭😭😭😭😭😭😭...
Imagine a simply supported beam of Length L subjected to a moving load. The beam is a bridge and the load is a vehicle. We want to calculate the maximum shear force due to the moving load at point L/4 from the left end of the beam. How do we go about doing that? The location of the moving load is not fixed, so we cannot just write the equilibrium equations for the beam, analyze it, get the support reactions, then calculate the shear at L/4. In such an analysis, where would we place the moving load? At the middle of the beam? somewhere else? where? How do we know that load location actually results in the max shear to develop at L/4? Therefore, the usual way of analyzing a beam does not work. That kind of analysis works only when the load is fixed in its location. But here the load does not have a fixed location, it could be anywhere on the beam. In this case, we need to come up with an algebraic equation for the shear force at point L/4 as a function of the position of the moving load. Let x denote the position of the load measured from the left end of the beam. The equation for shear, then, can be written as: V(x) = -x/L 0 < x < L/4 V(x) = 1 - x/L L/4 < x < L Using the above algebraic equation(s), we can determine the maximum shear values via differentiation. That is, V(x) attains its maximum value, when the derivative of the function goes to zero. Instead of dealing with differentiation and algebraic manipulation, simply, we can graph the above equations and use visual inspection to solve the problem. What does the graph of the above equation called? Shear Influence line.
@@DrStructure unfortunately, i did not get it yet no sense comes to mind,, really appreciate your explanation... But i will ask why we cannot simply take maxiumum vertical load of bridge ( self weight plus max live load expected) and design due to that load.
Let's ignore dead load for now and just focus on the live load, that is, let's focus on the vehicular (moving) load only. Where would you place that load in order to analyze and design the bridge?
@@DrStructure likewise in flat slab loads for example when there is a wall / partition need to be replaced anywhere over the slab i dont know where the occupants will need to place the wall in future as a kind of change the spaces / rooms, when designing that flat slap i have to give a distributed wall load over the complete area of the slap so slab is safe wherever the location of that wall.. Hope i delivered it clearly.
Live loads on building floors are quite different than vehicle loads on bridges. In most cases, it is a common practice to view floor live loads as uniformly distributed over a segment of the slab, unless the floor is expected to support a heavy piece of machinery, in which case it has to be treated as a point load. In bridges however, that kind of approach is not feasible. Are you suggesting that we take the load of the vehicle, turn it into a distributed load and place it over the entire length of the bridge?
Here are a few commercial bridge software options available for professional use. Depending on your location and university, you may be eligible to obtain one of the following tools at a discounted (educational) price: CSIBridge: Bridge Analysis, Design, and Rating www.csiamerica.com/products/csibridge AutoDesk Structural Bridge Design www.autodesk.com/products/structural-bridge-design/overview?term=1-YEAR&tab=subscription Larsa 4D Bridge Series www.larsa4d.com/products/features/4dbridge-overview.aspx There are others, which you should be able to find online via search.
Well illustrated with most of the calculations. I appreciate your work👏
What an amazing lecture
Thanks 😊 for providing these valuable vedios
Thanks
Thank you so much for this discussion. Well presented.
Well presented and can be understand due to animation completey different from school textbook
Thanku so much sir.Animation of the video is very helpful in understanding
Thank you so much.
very nice explanation
loved it
Thank you for sharing detail of the engineering calculation.
You are welcome.
Thank so much
Nice work
Great work with 99.9%
another 0.1% would be perfect If you show the truck or tandem moving inside the greatest area to decide the maximum value for height*point load. (Not shown at all but just one or two example initially)
Hi , please add lecture for. Design of reinforced concrete and lecture for design of steel structure
Quick question, what if the bridge consists of four steel girders like this example, but there it no splice (hinge reaction) and the interior support is a concrete pier bolted to the girders using bearing plates? Would the concrete pier be considered a fix support? If so, how would this change the influence lines?
Generally, that would be considered a pin support. If the connection is actually made so as to behave as a fixed support, then we would end up with two independent beams, one to the left of the support and one to the right of it.
If we view the connection as a pin support, without the splice, the beam becomes statically indeterminate. Its influence line would no longer consists of straight lines, rather it becomes nonlinear (curve) in shape.
Thank you for this lecture. Pls send video on how to go about this one also. I hope it will add on to know the difference between the two : ( splice) and pin connection.
God bless you
How to find the values of these lane loads? Do I need to memorize it or will it be given?If you've a lecture about this lane load plz provide the link this Will be very helpfull
The lane load values are given in the governing design specifications for the target geographic location. In the United States, the governing specifications for highway (bridge) design are provided by the American Association of State Highway and Transportation Officials (AASHTO).
The LRFD Bridge Design Specifications (published by AASHTO) provide the load details. You can download the table of contents of the specifications here:
store.transportation.org/Common/DownloadContentFiles?id=2049
As a professional engineer, you need to have access to relevant design codes and specifications. As a student, you either have access to the needed specifications or the load values are provided to you, depending on the course you are taking. In a structural analysis course, most often, the load values are provided. In a design course where getting accustomed to the use of code and specifications is a course objective, you will learn how to navigate the specifications in search of relevant information.
better than 4 years degree in university
Thank you, I like the way you explained the concept, please which software do you use to make the video interactive like you do ?
Thanks for the feedback. The bridge model was created using SketchUP and rendered and animated using Lumion. The lecture presentation was prepared and animated using Adobe Illustrator. The avatar was made and animated using Reallusion software suite. The various pieces of the presentation were put together for producing the final video using Camtasia Studio.
25:24 why did you draw bending moment at B, while we are looking for bending moment at D ? Also, what reason did you use to calculate bending moment by multiplying only 1 external force (unit force) on FBD by distance (3 m) neglecting contribution of 2 other external forces shown on particular FBD ? I think that part is unclear. Thanks.
@25:24 we are not drawing the bending moment diagram. Rather, we are drawing the influence line for the bending moment at B. That explains why we are using a unit load. An influence line is always drawn using a unit load.
@24:24, we assert that the beam's maximum negative moment could occur at point E or at point B. To decide which point controls the design, we must draw the moment influence line for each point and compare the two diagrams. The moment influence line for point E is shown @24:53. The moment influence line for point B is shown @26.04. Since a larger negative area is associated with the latter influence line, we conclude that the moment reaches its max negative value at point B.
Now we place all the applied loads on the governing influence line (point B) to determine the max negative bending moment value at that point.
Good day Dr. Structure! Could you please help me understand the following?
(1) At 21:00 why did we not consider vertical reaction Dy due to shear splice (internal hinge) as done at 21:32?
(2) In Influence Lines, the vertical distance = value of reaction (or) shear (or) moment. So, qualitatively, what does the area under the influence line represent?
(3) Why is the lane load categorized as transient load? Doesn't this value not change?
1) @21:00 the shear force at the hinge is not shown, because it is zero. We could have (should have) shown the force vector and then derived its zero value from the equilibrium equations.
2) The height of the influence line represents reaction and shear values, but not moment values. When dealing with moment, the influence line gives us the load pattern that causes max/min moment values at a given point, but we then need to analyze the beam under that pattern to actually determine the values. There is no meaningful qualitative interpretation for the area under the diagram.
3) By definition, Lane Load is attributed to a series of vehicular loads that move in close proximity of each other in such a manner that their weights can be treated/viewed as being uniformly distributed, more or less like a train on a track. Since the load is that of hypothetical vehicles, it is not a permanent fixture on the bridge, it falls under the transient label.
@@DrStructure Wow! For (2) you've clarified perfectly. I understand completely. For (3) I mistook the definition. My apologies. Its interesting to note that US aashto determines gaps between trucks/cars (say 10m gap) for designing. Canada on the other hand assumes a packed traffic jam for designing (no gap.
For (1), I am getting 4 equations for Sum Fy=0, Sum Mx=0:
Ay + By + Dy -1= 0,
(Ma eqn)= 4.5 - 9By - 12Dy = 0
(Mb eqn)= 9Ay - 4.5 - 3Dy = 0
(Md eqn)= 12Ay + 3By - 7.5 = 0
I thought shear splice generates/resists no moment therefore no Md marked.
Solving the above system of equations (either by hand or by an online tool (such as Wolframalpha or symbolab)) shows that Ay, By, Dy will be in terms of another unknown. Please help me if I've generated the system of equations correctly.
On Question 1, we cannot solve the problem (determine all the unknowns) by just examining segment AD. We need to bring segment DC into the formulation before we can calculate all the unknowns.
Given that the beam has an internal hinge at D, we need to write the equilibrium equations for both AD and DC.
Starting with segment DC (not shown in the video), we can see that the free-body diagram for the segment consists of two forces, the shear force at D and the reaction force at C. Let’s label these forces Dy and Cy. The equilibrium equations for the segment can be written as:
SUM of Fy: Dy + Cy = 0
SUM of Moments (about C): 12 Dy = 0
Solving these equations for the unknowns, we get Dy = 0 and Cy = 0. This means that the shear force at the hinge is zero. And more generally, the segment carries no internal force.
So now if we examine segment AD, knowing that there is no shear force at D, we arrive at the free-body diagram and the results shown in the video.
@@DrStructure Ohh So that's what I missed out. I was aware that internal hinge(s) help "convert" statistically indeterminate structures into determinate ones, I just thought we could analyze either section. Thank you for the detailed explanation Prof! You're amazing!
Correct me If I'm wrong. Are these four girders laterally supported (support in-between girders) called CROSS_BEAMS or DIAPHRAGMS? Are these girders sitting on PIER CAPS?
Yes, there are cross-beams laterally bracing the girders. The girders are resting on friction pads on the piers.
@@DrStructure Thanks.
Aren't the two middle girders to receive higher load than the two edged girders from the slab weight?
It depends on the location of the girders relative to the slab. Here, we are assuming that the slab has an overhang at either end. That extra weight of concrete makes the two exterior girders carry the same amount of load as the interior girders. If the exterior girders had been placed at the edge of the slab, then yes, they would have been subjected to less loads than the other girders.
@@DrStructure
I hope you don't get me wrong, I like your work, but the over hang doesn't seems to me to be like half of internal span, plus you must've mentioned the barriers weight on both sides.
Thanks for your great work, many students and even graduated engineers are getting benefit from your channel.
@@totticapitano1 yes you are right as the loads from footpath and crash barriars is also to be considered on external girders and also the loads due to cross girder on all girders is to considered.
@@Spatidar1994 For brevity, simplicity, and clarity of the presentation, for illustrating the essence of the lecture (influence line usage), several load sources have been excluded from this analysis.
Missed an important part. The loads on the concrete slab
I don't get it about support in diagram why
1 is fixed and other is kind of roller support
There is no fixed support here, there are only pin and roller supports. Regardless, the type of supports used in a structure is always a design decision. In this case, the engineer has made those decisions already, we are simply using the given information to analyze the bridge.
Thank you
Is it beam? or girders? it seems that you treat the structure as beams when you are using the influence line I am confused now
Please elaborate why you are making the distinction here?
In this lecture, we are discussing influence lines; we are not discussing the design of the structural members. Whether the member is a standard beam or a customized deeper beam (i.e., a girder) has no bearing in our analysis.
@@DrStructure I am making a distinction because the influence line of a beam is different on the influence line of a girder.
In the case of the bridge we are considering, that would be a distinction with no difference.
On the other hand, in the case of a floor girder where the girder is not a continuous beam, rather it is a series of simply supported beams, that distinction becomes relevant.
@@DrStructure Thankyou! now I understand
@@DrStructure I will take this chance to ask another question,
In a given beam, supports, and axle loads , How can we know the point on the beam where the maximum shear or moment will occur?
Could not get it yet from anywhere on youtube!! Influence line does not make any sense to me at all,, why we need it? What is the difference between this and the ordinary or usual way of calculating loads on beams???? If i have a beam with point load then its easy to get the reaction forces at supports whatever is the location of this load,, why there is a topic called influence line 😭😭😭😭😭😭😭...
Imagine a simply supported beam of Length L subjected to a moving load. The beam is a bridge and the load is a vehicle.
We want to calculate the maximum shear force due to the moving load at point L/4 from the left end of the beam. How do we go about doing that? The location of the moving load is not fixed, so we cannot just write the equilibrium equations for the beam, analyze it, get the support reactions, then calculate the shear at L/4. In such an analysis, where would we place the moving load? At the middle of the beam? somewhere else? where? How do we know that load location actually results in the max shear to develop at L/4? Therefore, the usual way of analyzing a beam does not work. That kind of analysis works only when the load is fixed in its location. But here the load does not have a fixed location, it could be anywhere on the beam.
In this case, we need to come up with an algebraic equation for the shear force at point L/4 as a function of the position of the moving load. Let x denote the position of the load measured from the left end of the beam. The equation for shear, then, can be written as:
V(x) = -x/L 0 < x < L/4
V(x) = 1 - x/L L/4 < x < L
Using the above algebraic equation(s), we can determine the maximum shear values via differentiation. That is, V(x) attains its maximum value, when the derivative of the function goes to zero.
Instead of dealing with differentiation and algebraic manipulation, simply, we can graph the above equations and use visual inspection to solve the problem. What does the graph of the above equation called? Shear Influence line.
@@DrStructure unfortunately, i did not get it yet no sense comes to mind,, really appreciate your explanation... But i will ask why we cannot simply take maxiumum vertical load of bridge ( self weight plus max live load expected) and design due to that load.
Let's ignore dead load for now and just focus on the live load, that is, let's focus on the vehicular (moving) load only. Where would you place that load in order to analyze and design the bridge?
@@DrStructure likewise in flat slab loads for example when there is a wall / partition need to be replaced anywhere over the slab i dont know where the occupants will need to place the wall in future as a kind of change the spaces / rooms, when designing that flat slap i have to give a distributed wall load over the complete area of the slap so slab is safe wherever the location of that wall.. Hope i delivered it clearly.
Live loads on building floors are quite different than vehicle loads on bridges. In most cases, it is a common practice to view floor live loads as uniformly distributed over a segment of the slab, unless the floor is expected to support a heavy piece of machinery, in which case it has to be treated as a point load. In bridges however, that kind of approach is not feasible. Are you suggesting that we take the load of the vehicle, turn it into a distributed load and place it over the entire length of the bridge?
what voice software did you use?
It is human voice.
Avec quel logiciel peut on faire un tel design svp?
Do you mean bridge design or lecture design?
@@DrStructure bridge design.
I have to design a bridge which is exposed to hazards, for my Final thesis in civil engineering.
Here are a few commercial bridge software options available for professional use. Depending on your location and university, you may be eligible to obtain one of the following tools at a discounted (educational) price:
CSIBridge: Bridge Analysis, Design, and Rating
www.csiamerica.com/products/csibridge
AutoDesk Structural Bridge Design
www.autodesk.com/products/structural-bridge-design/overview?term=1-YEAR&tab=subscription
Larsa 4D Bridge Series
www.larsa4d.com/products/features/4dbridge-overview.aspx
There are others, which you should be able to find online via search.
@@DrStructure thank you for your support. I'll chek on them.
I bet that teaching stick she using could reach the moon's surface with no problems