We have two equations in two unknowns: 0.24 d1 - 0.063 d2 = 5 EA -0.063 d1 + 0.298 d2 = -8 EA Solving them for d1 and d2, we get: d1 = 14.59/EA and d2 = -23.75/EA The use of the matrix displacement method requires knowledge of linear algebra. Without knowing how to solve systems of linear equations, you will not be able to analyze structures using this method.
E is the modulus of elasticity of the material and I is the moment of inertia of the member about its axis of bending. These values depend on the type of material being used and the (cross sectional) sizes of the structural members. Generally, we use them at the beginning of the process, especially if the structural consists of multiple member sizes or materials.
im confused, im plugging in the values for cos(theta) testing if you got it right, but i get values like 0.72, not 0.072. Or sometimes i'm getting half your result, like 0.36 instead of 0.072. Do you know what i'm doing wrong? :/.
The values are given in the video are cosine and sine divided by L. Note that the matrix has (EA/L) as a multiplier. Here, we are dividing the elements of each member stiffness matrix by L in order to facilitate the compositing of the system stiffness matrix.
Dr. Structure oh yeah I forgot about the EA/L factored outside. No worries. I don’t understand how this channel hasn’t exploded. This channel has every topic covered so thoroughly for structural engineering students it’s absolutely incredible. I am studying for a test in two days on-indeterminate structures and I feel I get it, pretty well actually. Thanks again !!
The displacement method can be easy modified to take into account secondary loads. For example, if a truss member goes through a temperature change, its length wants to change in relation to the change in temperature and the coefficient of thermal expansion. The change in length equal: (Thermal Expansion Coefficient)(Temperature Change)(Member Length). This change in length times EA for the member gives the force in the member caused by the change in temperature. We can then translate this member force into nodal loads (at the ends of the member) and proceed as if they were actually applied loads. We calculate the system stiffness as before and solve the resulting system of equations for the nodal displacement...
Good day Dr Structure, i am emailing a problem that i am busy solving it that has a support settlement. So my challenge is how to involve it on the calculations coz at the end its not giving me the correct reaction especially the directions
@@DrStructure Thank you Dr Structure. My problem has been finally solved, i have finally seen where i was making a mistake, and also the final treatment of the settlement that i would not ever had known.
Sure, we will post another truss analysis example using the displacement method in couple of days. Yes, it need to be in pdf format as such a video production is quite time consuming.
@@DrStructure Thank you so, its very helpful, i had not realized that you had sent it because i had not received an email as notification. But otherwise i thank you once again.
I am fan of Dr. Structure it gives imagination a picture of reality.
here remembering structural analysis, and thanks for such a good explanation, 100 points.. New subscriber
great video, super easy to understand matrix displacement method
Excellent video!
Great video 👍
@ 12:02 how did you get the 14.59 and -23,75
We have two equations in two unknowns:
0.24 d1 - 0.063 d2 = 5 EA
-0.063 d1 + 0.298 d2 = -8 EA
Solving them for d1 and d2, we get:
d1 = 14.59/EA and d2 = -23.75/EA
The use of the matrix displacement method requires knowledge of linear algebra. Without knowing how to solve systems of linear equations, you will not be able to analyze structures using this method.
@@DrStructure thank you, brainstormed it and realize I have to use simultaneous equations
greetings I was wondering, if you have a IE value when is the safest time to enter the values?
E is the modulus of elasticity of the material and I is the moment of inertia of the member about its axis of bending. These values depend on the type of material being used and the (cross sectional) sizes of the structural members. Generally, we use them at the beginning of the process, especially if the structural consists of multiple member sizes or materials.
Thank you for replying so quickly have an online exam today.... appreciate it 👍🏾
im confused, im plugging in the values for cos(theta) testing if you got it right, but i get values like 0.72, not 0.072. Or sometimes i'm getting half your result, like 0.36 instead of 0.072. Do you know what i'm doing wrong? :/.
The values are given in the video are cosine and sine divided by L. Note that the matrix has (EA/L) as a multiplier. Here, we are dividing the elements of each member stiffness matrix by L in order to facilitate the compositing of the system stiffness matrix.
Dr. Structure oh yeah I forgot about the EA/L factored outside. No worries. I don’t understand how this channel hasn’t exploded. This channel has every topic covered so thoroughly for structural engineering students it’s absolutely incredible. I am studying for a test in two days on-indeterminate structures and I feel I get it, pretty well actually. Thanks again !!
@dr.structure how to incorporate indirect loading like misfit load due to temperature in stiffness method In truss
The displacement method can be easy modified to take into account secondary loads. For example, if a truss member goes through a temperature change, its length wants to change in relation to the change in temperature and the coefficient of thermal expansion. The change in length equal: (Thermal Expansion Coefficient)(Temperature Change)(Member Length). This change in length times EA for the member gives the force in the member caused by the change in temperature. We can then translate this member force into nodal loads (at the ends of the member) and proceed as if they were actually applied loads. We calculate the system stiffness as before and solve the resulting system of equations for the nodal displacement...
Good day Dr Structure, i am emailing a problem that i am busy solving it that has a support settlement. So my challenge is how to involve it on the calculations coz at the end its not giving me the correct reaction especially the directions
Your solution looks good. You probably have made a mistake in solving the linear system of equations. Please check your email for additional details.
@@DrStructure Thank you Dr Structure. My problem has been finally solved, i have finally seen where i was making a mistake, and also the final treatment of the settlement that i would not ever had known.
thx for this good video..
Good day Dr Structure
Is it possible to get me another exam of the nature, even in pdf format.
Sorry i wanted to say example instead of exam on my message above.
Sure, we will post another truss analysis example using the displacement method in couple of days. Yes, it need to be in pdf format as such a video production is quite time consuming.
@@DrStructure okay, thanks. I will be waiting for it.
Here is the link to the pdf: lab101.space/pdf/examples/SA48-TrussAnalysisExample.pdf
@@DrStructure Thank you so, its very helpful, i had not realized that you had sent it because i had not received an email as notification. But otherwise i thank you once again.
Beautiful
Hi sir, why chapter 47 is missing
th-cam.com/video/eKQBjpHypzk/w-d-xo.html
@@DrStructure thanks, i think the link from lab101.space for lecture 47 need to be fixed, it links me to chapter 48, just fyi :D
Thanks, we'll make the correction.
i came here for one semester "structure analysis"
Plz make videos on shear center, shear flow, how to calculate shear center for thin open and closed sections and stuff...plz....
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