The following python code is meant to take any truss, inputting information about its nodes, members, and external loads and the code is meant to output all internal member forces and reactions of the truss.

Task: Add a virtual work method where the horizontal and vertical deflection can be calculated and outputted. The code should be able to output the horizontal and vertical deflection of any node in the truss.

Fix any errors in this code. Once you finish, submit the finished python code and ensure it works. I will check the code to see if it is right. If everything is good, I will give you a like immediately.

If the submitted code can$$t run, I will give you a thumbs down, until it is fixed.

Python Code $>$

import numpy as np

class Truss:

def $\_\_$init$\_\_($self$,$ nodes, members, loads$)$:

self.nodes $=$ nodes

self.members $=$ members

self.loads $=$ loads

self.num$\_$nodes $=$ len$($nodes$)$

self.num$\_$members $=$ len$($members$)$

self.num$\_$unknowns $=$ self.num$\_$members $*2$ # Each member has two unknown forces

def solve$\_$method$\_$of$\_$joints$($self$)$:

# Initialize the equations matrix and the forces vector

num$\_$equations $=$ self.num$\_$nodes $-1$ # Number of equations

A $=$ np$.$zeros$(($num$\_$equations, self.num$\_$unknowns$))$

forces $=$ np$.$zeros$(($num$\_$equations, $1))$

# Fill the equations matrix and forces vector

eq$\_$index $=0$ # Equation index

for node in self.nodes:

if node $!=$ 'fixed': # Skip the fixed node

# Gather member indices connected to the current node

member$\_$indices $=[$i for i$,$ member in enumerate$($self$.$members$)$ if node in member$[\text{'}$nodes$\text{'}]]$

# Sum forces in x and y directions for each connected member

for member$\_$index in member$\_$indices:

dx $=$ self.nodes$[$self$.$members$[$member$\_$index$][\text{'}$nodes$\text{'}][1]][\text{'}$x$\text{'}]-$ self.nodes$[$self$.$members$[$member$\_$index$][\text{'}$nodes$\text{'}][0]][\text{'}$x$\text{'}]$

dy $=$ self.nodes$[$self$.$members$[$member$\_$index$][\text{'}$nodes$\text{'}][1]][\text{'}$y$\text{'}]-$ self.nodes$[$self$.$members$[$member$\_$index$][\text{'}$nodes$\text{'}][0]][\text{'}$y$\text{'}]$

length $=$ np$.$sqrt$($dx$**2+$ dy$**2)$

cos$\_$theta $=$ dx $/$ length

sin$\_$theta $=$ dy $/$ length

A$[$eq$\_$index, $2*$ member$\_$index$]=$ cos$\_$theta

A$[$eq$\_$index, $2*$ member$\_$index $+1]=$ sin$\_$theta

# Add external forces to the forces vector

for load in self.loads:

if load$[\text{'}$joint$\text{'}]==$ node:

forces$[$eq$\_$index$]=$ load$[\text{'}$force$\text{'}]$

eq$\_$index $+=1$

try:

# Solve for the unknown forces

unknown$\_$forces $=$ np$.$linalg.lstsq$($A$,$ forces, rcond$=$None$)[0]$

except np$.$linalg.LinAlgError:

print$("$Error: Incompatible dimensions in the linear equations."$)$

return None

# Store the results in a dictionary

results $=\{\}$

for i$,$ member in enumerate$($self$.$members$)$:

results$[$member$[\text{'}$name$\text{'}]]=\{$

'force$\_$x$\text{'}$: unknown$\_$forces$[2*$ i$,0],$

'force$\_$y$\text{'}$: unknown$\_$forces$[2*$ i $+1,0]$

$\}$

return results

# Example usage:

nodes$1=\{\text{'}$A$\text{'}$: $\{\text{'}$x$\text{'}$: $0,\text{'}$y$\text{'}$: $0\},\text{'}$B$\text{'}$: $\{\text{'}$x$\text{'}$: $0,\text{'}$y$\text{'}$: $3\},\text{'}$C$\text{'}$: $\{\text{'}$x$\text{'}$: $4,\text{'}$y$\text{'}$: $0\}\}$

members$1=[\{\text{'}$name$\text{'}$: $\text{'}$AB$\text{'},$ 'nodes': $[\text{'}$A$\text{'},\text{'}$B$\text{'}]\},\{\text{'}$name$\text{'}$: $\text{'}$BC$\text{'},$ 'nodes': $[\text{'}$B$\text{'},\text{'}$C$\text{'}]\}]$

loads$1=[\{\text{'}$force$\text{'}$: $100,$ 'delta$\_$x$\text{'}$: $0,$ 'delta$\_$y$\text{'}$: $3,$ 'joint': $\text{'}$B$\text{'}\}]$

truss $=$ Truss$($nodes$1,$ members$1,$ loads$1)$

# Solve for unknown forces using Method of Joints

results $=$ truss.solve$\_$method$\_$of$\_$joints$()$

if results is not None:

print$("$Unknown forces:"$)$

for member, forces in results.items$()$:

print$($f$"\{$member$\}$: $\{$forces$\}")$