This document summarizes a group project analyzing the loading on an airplane floor beam. The group determined the shear force, bending moment, slope, and deflection along the beam due to a distributed load. They also calculated the reactions at the supports using equilibrium equations and the singularity method. Plots of the load, shear force, and bending moment diagrams were produced. Stress elements and Mohr's circle were also used to analyze the original stresses in the beam.

1. PRACTICAL APPLICATION
MECHANICS OF MATERIAL

2. GROUP MEMBERS:
 ARSLAN ZAFAR 15-ME-019
 ZEESHAN RASOOL 15-ME-047
 ABDULLAH KHALID 15-ME-075
 MUAZ ALI 15-ME-079

3. PROBLEM :
THE LOADING ON A FLOOR BEAM USED IN THE AIR-PLANE IS SHOWN. USE
SPECIAL FUNCTION TO REPRESENT THE DISTRIBUTED LOAD AND DETERMINE THE
DISTRIBUTION OF
 SHEAR FORCE
 MOMENT
 SLOPE
 DEFLECTION
ALONG THE BEAM. FINALLY DETERMINE THE REACTIONS AT THE SUPPORTS A
AND B. WHERE THE MODULUS OF ELASTICITY IS 29*E9psi AND AREA MOMENT
OF INERTIA ABOUT THE AXIS OF BENDING IS 272 in^4.

5. SOLUTION:

6. FIGURE:

7. FREE BODY DIAGRAM:

8. EQUILIBRIUM EQUATIONS:
𝜮𝑭 𝑿 = 𝟎
𝑅 𝑎𝑥 = 0
𝜮𝑭 𝒀 = 𝟎
𝑅 𝐴 + 𝑅 𝐵 − 3600 = 0
𝑅 𝐴 + 𝑅 𝐵 = 3600
𝜮𝑴 𝑨 = 𝟎
𝑀𝐴 − 30 ∗ 120 ∗ 60 + 𝑅 𝐵 ∗ 240 = 0
𝑀𝐴 + 240𝑅 𝐵 = 216000

9. DEGREE OF BEAM:
DOB = # OF UN-KNOWNS - # OF EQUATIONS
= 3 – 2
= 𝟏 𝒔𝒕 𝑫𝑬𝑮𝑹𝑬𝑬 𝑺𝑻𝑨𝑻𝑰𝑪𝑨𝑳𝑳𝒀 𝑰𝑵𝑫𝑬𝑻𝑬𝑹𝑴𝑰𝑵𝑨𝑻𝑬 𝑩𝑬𝑨𝑴

10. SINGULARITY METHOD:

11. CONDITIONS:

12. EQUATION OF ELASTIC CURVE:
𝐸𝐼
𝑑2
𝑦
𝑑𝑥2
= 𝑀(𝑥)

17. LOAD DIAGRAM:

18. SHEAR FORCE DIAGRAM:

19. BENDING MOMENT DIAGRAM:

20. STRESS ELEMENT:

21. MOHAR CIRCLE:

23. CONCLUSION:
IN THIS DESIGN THE BEAM IS TAKEN FROM THE SMALL PORTION OF AN AIR CRAFT WHICH IS
ACTUALLY A REAL LIFE APPLICATION OF AN AEROSPACE.
THERE IS UNIFORM DISTRIBUTED LOAD ON HALF PORTION OF THE BEAM WHOSE
RESULTANT IS LOACTED AT THE CENTROID.
IT IS STATICALLY INDETERMINATE BEAM WHICH CAN BE SOLVE BY MAKING IT DETERMINATE.
WE USE SINGULARITY METHOD BECAUSE IT IS THE EASIEST AND MOST ACCURATE METHOD
TO HANDLE.
BY SOLVING THE BEAM; WE HAVE DRAWN THE SHEAR FORCE AND BENDING MOMENT
DIAGRAM FROM THE LOAD DIAGRAM.
WE ALSO DETERMINE THE STRESS ELEMENTS.
AT THE END WE DRAW THE MOHAR CIRCLE WHICH IS SHOWING THE ORIGNAL STATE OF
STRESSES.

24. REFRENCES:
 Https://bendingmomentdiagram.com/free-calculator/
 https://bendingmomentdiagram.com/free-calculator/mohrs-
circle-calculator/

25. THANK YOU