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   "source": [
    "# Chapter 13 Principle of Virtual Work"
   ]
  },
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   "source": [
    "# Example 13.1 Application of Principle of Virtual Work"
   ]
  },
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     "text": [
      "The value of force (i.e P) that can hold the system in equilibrium is 500 N\n"
     ]
    }
   ],
   "source": [
    "# Initilization of variables\n",
    "W=1000 # N # weight to be raised\n",
    "# Calculations\n",
    "# From the Principle of virtual work,\n",
    "P=W/2 # N\n",
    "# Results\n",
    "print('The value of force (i.e P) that can hold the system in equilibrium is %d N'%P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 13.7 Application of Principle of Virtual Work"
   ]
  },
  {
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   "execution_count": 6,
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     "text": [
      "The Horizontal component of reaction at A (X_A) is 333.333333 N\n",
      "The Vertical component of reaction at A (Y_A) is 1333.333333 N\n",
      "The Horizontal component of reaction at B (X_B) is 333.333333 N\n",
      "The Vertical component of reaction at B (Y_B) is 666.666667 N\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "# Initilization of variables\n",
    "P=1000 # N # Force acting at the hinge of the 1st square\n",
    "Q=1000 # N # Force acting at the hinge of the 2nd square\n",
    "# Calculations\n",
    "# Chosing the co-ordinate system with originat A, we can write,\n",
    "theta=45 # degree\n",
    "# Forces that do work are P,Q & X_B. Applying the principle of virtual work & Simplyfying and solving for X_B,\n",
    "X_B=((2*P)/6)*(math.cos(theta*math.pi/180)/math.sin(theta*math.pi/180)) # N \n",
    "# Now give a virtual angular displacement to the whole frame about end A such that line AB turns by an angle delta_phi.\n",
    "# The force doing work are P,Q&Y_B.Applying the principle of virtual work & Simplyfying this eq'n and solving for Y_B,\n",
    "Y_B=((3*Q)+P)/6 # N\n",
    "# Simply by removing the support at A & replacing it by the reactions X_A & Y_A we can obtain,\n",
    "X_A=X_B # N\n",
    "Y_A=P+Q-Y_B # N\n",
    "# Results\n",
    "print('The Horizontal component of reaction at A (X_A) is %f N'%X_A)\n",
    "print('The Vertical component of reaction at A (Y_A) is %f N'%Y_A)\n",
    "print('The Horizontal component of reaction at B (X_B) is %f N'%X_B)\n",
    "print('The Vertical component of reaction at B (Y_B) is %f N'%Y_B)"
   ]
  }
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