These lectures are not done based on a specific textbook. But I recommend Matrix Analysis of Structures by Aslam Kassimali. It is a good introductory text on the subject.
Hey Doc. This channel is the most beautiful channel I have ever seen in this field. I appriciate your work. (By the way at 13:37 the direction of the moment at the right hand side of fixed support A is should be the opposite)
We know k12 = k21. So, let's call this stiffness coefficient K. We can view K as a converter coefficient. It converts vertical displacement in direction 1 to bending moment in direction 2. And, it converts rotation in direction 2 to vertical force in direction 1. So, when we multiply K by d1 (displacement in direction 1), we we get bending moment f2. And when we multiply it by d2, we get vertical force f1. The same happens at the other end of the beam with k34.
0:59 For slope deflection method I was assuming clockwise moments as positive and shear forces as per positive sign convention(upward shear force @left end of the beam element and downward shear force @right end of the beam element) will this make any difference in the results or anywhere in between the process (that you have shared here) if I stick w/ the same sign convention for matrix displacement method?
Your sign convention is okay, but since the derivation for the matrix method was done based on a different (opposite) sign convention, you may run into a slight problem at the end. It would be best if you utilized the assumed sign convention, if you are going to use the formulation presented here. I would also like to mention that one should not mix/confuse the beam sign convention with the sign convention we use in these methods. For example, in the slope-deflection method as well as the matrix method, we assume the member-end moment to be positive when counterclockwise (at both ends of the member). This is not to be confused with the beam sign convention according to which positive moment means, a clockwise moment at the left end of the segment and a counterclockwise moment at the right end of the segment (the moment pair that causes the beam to bend concave up is considered positive).
I was totally confused. So is it like I should better accustomed to this sign convention and should only use it for solving any such sort of problems now? 'cause if I go back and solve slope deflection method with this sign convention I might loose track for now , at least I feel so!
The matrix method is based on the slope-deflection method. So, in principle, they both use the same sign convention. That is, we assume counterclockwise rotation and moment at each member end to be positive. That is it, that is the sign convention for the slope-deflection method which is consistent with the sign convention for the matrix method. Yes, it would be best if you adhere to the prescribed sign convention here, and try to resolve the differences that you see between the two methods in this regard.
Perfect explanation and helpful. The only thing i didn't understood was why did you used the 2 moments as 0 when there is point load of 10kn, shouldn't this load create a moment in joint b and c?
@12:20 the rotation in direction 2 is set to zero, since at the fixed end of the beam (at A) rotation is in fact zero. That does not mean bending moment is zero, it simply means the beam is not going to rotate at that point. When setting up the problem using the displacement method, we make no assumptions about internal forces of the members, we simply observe the (displacement) boundary conditions when numbering the degrees of freedom of the system.
@@DrStructure thank you for taking your time to respond. 2 forces i was referring are 7:26, but from your post i understand in fix supports rotation are zero and moment has value and in pin support rotation is not zero but moment is zero.
Correct. @7:26 we are writing the vector of the applied forces (these are not internal forces in the beam, they are the forces we've placed on the beam). In this case, since the beam is subjected to only one force, the other components of the vector are zero. If there was an applied moment at B and/or at C, then we would have used their values instead of zero when writing the force vector.
You should be able to find an explanation for this in most structural analysis textbooks that deal with the matrix method. See Structural Analysis by R.C. Hibbeler, for example.
See Exercise Problem 1 at the end of the video, click on the i at the upper right corner of the screen to access the solution to the exercise problem. Also, see Lecture SA50.
Material and section properties are used for calculating the member stiffness coefficients. So different values for E and I impact the computed k values for each member.
If you want to solve the equations using hand calculations, I suggest using the Gaussian Elimination Method. Alternatively, you can use software tools such as Mathematica to tackle the problem.
Can I get the reference book for this lectures?
These lectures are not done based on a specific textbook. But I recommend Matrix Analysis of Structures by Aslam Kassimali. It is a good introductory text on the subject.
This is revolutionary. Thank you, from the bottom of my heart!
Hey Doc. This channel is the most beautiful channel I have ever seen in this field. I appriciate your work. (By the way at 13:37 the direction of the moment at the right hand side of fixed support A is should be the opposite)
Thanks for the note. Yes, that moment is drawn incorrectly.
this is so lucid.😭I love you !
@13:39, the moment of fixed support A should be counterclockwise in direction.
Perfect! Thanks or the correction.
Hi Dr. Structure, I think at 4:28, k12d2 should be a bending moment instead of a vertical force. Isn’t it? Regards
We know k12 = k21. So, let's call this stiffness coefficient K.
We can view K as a converter coefficient. It converts vertical displacement in direction 1 to bending moment in direction 2. And, it converts rotation in direction 2 to vertical force in direction 1.
So, when we multiply K by d1 (displacement in direction 1), we we get bending moment f2. And when we multiply it by d2, we get vertical force f1.
The same happens at the other end of the beam with k34.
Dr. Structure Thank you so much for the clarification.
You are welcome. :)
0:59 For slope deflection method I was assuming clockwise moments as positive and shear forces as per positive sign convention(upward shear force @left end of the beam element and downward shear force @right end of the beam element) will this make any difference in the results or anywhere in between the process (that you have shared here) if I stick w/ the same sign convention for matrix displacement method?
Your sign convention is okay, but since the derivation for the matrix method was done based on a different (opposite) sign convention, you may run into a slight problem at the end. It would be best if you utilized the assumed sign convention, if you are going to use the formulation presented here.
I would also like to mention that one should not mix/confuse the beam sign convention with the sign convention we use in these methods. For example, in the slope-deflection method as well as the matrix method, we assume the member-end moment to be positive when counterclockwise (at both ends of the member). This is not to be confused with the beam sign convention according to which positive moment means, a clockwise moment at the left end of the segment and a counterclockwise moment at the right end of the segment (the moment pair that causes the beam to bend concave up is considered positive).
I was totally confused. So is it like I should better accustomed to this sign convention and should only use it for solving any such sort of problems now? 'cause if I go back and solve slope deflection method with this sign convention I might loose track for now , at least I feel so!
The matrix method is based on the slope-deflection method. So, in principle, they both use the same sign convention. That is, we assume counterclockwise rotation and moment at each member end to be positive. That is it, that is the sign convention for the slope-deflection method which is consistent with the sign convention for the matrix method.
Yes, it would be best if you adhere to the prescribed sign convention here, and try to resolve the differences that you see between the two methods in this regard.
Dr. Structure Thank you! When will you be releasing lectures on reinforced concrete design? Anytime soon??
Probably not soon enough. There is a lot of ground to cover before we get there.
Perfect explanation and helpful. The only thing i didn't understood was why did you used the 2 moments as 0 when there is point load of 10kn, shouldn't this load create a moment in joint b and c?
@12:20 the rotation in direction 2 is set to zero, since at the fixed end of the beam (at A) rotation is in fact zero. That does not mean bending moment is zero, it simply means the beam is not going to rotate at that point. When setting up the problem using the displacement method, we make no assumptions about internal forces of the members, we simply observe the (displacement) boundary conditions when numbering the degrees of freedom of the system.
@@DrStructure thank you for taking your time to respond. 2 forces i was referring are 7:26, but from your post i understand in fix supports rotation are zero and moment has value and in pin support rotation is not zero but moment is zero.
Correct. @7:26 we are writing the vector of the applied forces (these are not internal forces in the beam, they are the forces we've placed on the beam). In this case, since the beam is subjected to only one force, the other components of the vector are zero. If there was an applied moment at B and/or at C, then we would have used their values instead of zero when writing the force vector.
@@DrStructure well understood. Thank you really appreciate your efforts guys. You don't know how much you really helping people. Thank you again
@@sulaimansamatar4459 You're welcome!
at 13:09 k12 of member bc is 2EI
At 13:39, one of the moments at point A might be pointed to the wrong direction.
Yes, you are right. The internal moment acts in the opposite direction to what is shown. Thanks or the correction.
I suppose the direction of the reaction moment is correct while the inner moment shown in the figure is incorrect.
How do we analyse a beam with an internal hinge?
This will be explained in a future lecture.
Will you upload for frame ? I would like to study . Thank you.
Can the numbering be done in any order?
Yes, there is no specific order to numbering the degrees of freedom.
Can I find the solution of the hometask you gave?
The solutions are provided in the (free) online course referenced in the video description field.
Can you please tell me any reference source :textbook, website etc from where I can learn to determine the kinematic indeterminacy of structures?
You should be able to find an explanation for this in most structural analysis textbooks that deal with the matrix method. See Structural Analysis by R.C. Hibbeler, for example.
Dr. Structure Thank you. Dr structure team rocks!!
Thank you for the feedback.
if there is a distribution load on a member of the system , how can i solve it ?
See Exercise Problem 1 at the end of the video, click on the i at the upper right corner of the screen to access the solution to the exercise problem. Also, see Lecture SA50.
What if the members have different El?
Material and section properties are used for calculating the member stiffness coefficients. So different values for E and I impact the computed k values for each member.
are there solutions to the examples at the end?
Click on the circled i at the upper right corner of the video. You can also find the links in the video description field.
How do you solve the equations?
If you want to solve the equations using hand calculations, I suggest using the Gaussian Elimination Method. Alternatively, you can use software tools such as Mathematica to tackle the problem.
Dear Admin,
I’m really grateful for ur good work..can u please upload “BEAM ANALYSIS USING STIFFNESS METHOD”
Thank you so much 🙏
Stiffness method and displacement method are one and the same.