I Used Python to Compute the Deflection and Axial Forces of a Truss Bridge

I wrote a python program that calculates a truss bridge's axial stresses and deflection by implementing the virtual work principle.

To compute the deflection of a truss structure at any nodal point, we first have to compute the axial forces due to the external loads applied to the structure. Then, remove the external loads and replace them with a unit virtual load where the deflection is to be obtained.

we will be using a python library called anastruct for the structural analysis of our structure.

anastrcut is a python library for the implementation of the 2D Finite Element method for structures. It allows you to do a structural analysis of frames and trusses. It helps you to compute the stresses and displacements in structural elements.

This Instructable is important because analysis of a structure like a truss is time-consuming and students in the field of structural engineering are bound to make errors. Hence, developing programs like this will help them in validating their answers

1. Personal computer
2. Google colab for writing and running code
3. Install the anaStruct library
4. pandas library
5. Question from structville website: as shown from the picture above, we are asked to compute the deflection at point c using the virtual work method

For us to start building the model, we need to install the anaStruct library.

pip install anastruct

Then we build our Truss model by instantiating the structure object. This is implemented by importing systemElements class from the anastruct library and instantiating it.

Then we can access all the structure objects states, including elements, materials and forces.

#lets import the systemElemnts from the anastruct libraryfrom anastruct import SystemElements#instatiate the SystemElement objectss = SystemElements()#lets add truss members at node using add_truss_element method and passing coordinate loaction as argument to #define length of each memberss.add_truss_element(location=[[0, 0], [3, 0]])ss.add_truss_element(location=[[0, 0], [3, 3]])ss.add_truss_element(location=[[3, 3], [3, 0]]) ss.add_truss_element(location=[[3, 0], [6, 3]])ss.add_truss_element(location=[[3, 0], [6, 0]])ss.add_truss_element(location=[[3, 3], [6, 3]])ss.add_truss_element(location=[[6, 3], [6, 0]])ss.add_truss_element(location=[[6, 3], [9, 3]])ss.add_truss_element(location=[[6, 0], [9, 3]])ss.add_truss_element(location=[[6, 0], [9, 0]])ss.add_truss_element(location=[[9, 0], [9, 3]])#this method plot our assemble structuress.show_structure()

What this code will be doing is adding support conditions to our truss model

# Add support condition#the add_support_hinged function is used to specify hinge support#the node_id argument is the nodal position at which the  support is placed which is an intergerss.add_support_hinged(node_id=1) #the add_support_roll method is used to specify roller supportss.add_support_roll(node_id=7)

okay lets add some point and horizontal loads to our model

# Add loadings#the point_load method indicate it is a point load #the argument fy indicate it is a vertical force and negative sign indicate downard acting at node 4ss.point_load(Fy=-6, node_id=3) #acting at node 4ss.point_load(Fy=-4, node_id=4)#Fx is a horizontal force acting in the positive direction at node 6ss.point_load(Fx=+10, node_id=6)

lets calcuate our axial forces in the members due to external load and plot the result

#this method compute all the reaction forces and axial forces in the modelss.solve()#this method plot the computed axial forces of the truss elements or members  ss.show_axial_force()

lets plot our reaction forces at our supports

#this method plot the computed reaction forces at the supportss.show_reaction_force()

let's show how our truss model will be displaced due to externally applied load

#this method plot the computed displacement of the entire model.ss.show_displacement(factor=15)

we are replacing all external load and placing a virtual unit load at node 2 which is equivalent to node c from the original question

# we are creating another model and giving it a virtual#this method reset the structure and remove the external applied loadsss.remove_loads()ss = SystemElements()ss.add_truss_element(location=[[0, 0], [3, 0]])ss.add_truss_element(location=[[0, 0], [3, 3]])ss.add_truss_element(location=[[3, 3], [3, 0]])ss.add_truss_element(location=[[3, 0], [6, 3]])ss.add_truss_element(location=[[3, 0], [6, 0]])ss.add_truss_element(location=[[3, 3], [6, 3]])ss.add_truss_element(location=[[6, 3], [6, 0]])ss.add_truss_element(location=[[6, 3], [9, 3]])ss.add_truss_element(location=[[6, 0], [9, 3]])ss.add_truss_element(location=[[6, 0], [9, 0]])ss.add_truss_element(location=[[9, 0], [9, 3]])#dd suupportss.add_support_hinged(node_id=1)ss.add_support_roll(node_id=7)#Add method add the  virtual unit load at node2ss.point_load(Fy=-1, node_id=2)ss.show_structure()#we compute our member axial forces and reactions forces due to virtual unit loadss.solve()

we are saving our computation from the returned type of the get_element_result method which is a python list of dictionary

#this method store our calculation result of our elements or members in list of dictionarylist_ext=ss.get_element_results(element_id=0)#this method returns a list of dictionary with our computed forces due to virtual load and we pass it to variablelist_vir=ss.get_element_results(element_id=0)

we are using the pandas data frame to store our results

# we import pandas and create a table for all our computed resultsimport pandas as pd#we create an empty dataframe for storing our computed result due to external loadsdf=pd.DataFrame()#we create an empty dataframe for storing our computed result due to virtual unit loadpf=pd.DataFrame()#we store our computed result due to external loads that return as a list of dictionary into a dataframedf = df.append(list_ext, ignore_index=True, sort=False)#we drop the 'alpha' and 'u' columndf.drop(['alpha', 'u'], axis = 1, inplace = True)#we rename our dataframe columns df.rename(columns={'length': 'L(m)',                   'N': 'N(kN)',                   'id':'Members'},          inplace=True, errors='raise')#we store our computed result due to virtual unit load that return as a list of dictionary into another dataframepf = pf.append(list_vir,ignore_index=True, sort=False)#we drop or delete 'alpha', 'u','length'columnspf.drop(['alpha', 'u','length'], axis = 1, inplace = True) #we rename column'N' to 'n' pf.rename(columns={'N': 'n'},          inplace=True, errors='raise')#we use the concat method to combine our two dataframe df1= pd.concat([df, pf], axis=1, join='inner')#we move columnsnew_cols = ["Members","n","N(kN)","L(m)"]df1=df1[new_cols]#we multipy column n, N and L and create column nNL/AEdf1["nNL/AE"]= (df1["n"] * df1["N(kN)"] * df1["L(m)"])#we use the display method to show our final dataframe tabledisplay(df1.round(3))

The first table above is the author's solution from the structville website and the second table is my program computed table

Let's finally compute our deflection and compare it with one from the example

#we compute deflection at node 2deflection = df1["nNL/AE"].sum()print("The vertical deflection at node 2 is :",deflection.round(3),"/AE meters")#output from the program87.255/AE meters#result from the example in the article86.904/AE meters

From this instructable, it is possible to use the virtual force method to compute the deflection of a truss bridge using python programming. This is very important for students taking structural analysis courses to be able to very their assignment answers. You can run the code here

My future work will be focusing on creating a user interface for drawing the truss, frames and beams in 2d as the input for the structural analysis programs