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PSUEngineer09
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I'm trying to study for an exam, and there are a few problems that i cannot figure out:
1) A rigid beam is supported at point B by a pin/hole connection and by two cables at points A and C, respectively.
Initially (before load P is applied), there is no slack nor tension in either of the two cables. Under influence of load "P" both cables will be under tension and the beam will have rotated slightly in counter-clockwise direction. Neglect the weight of the beam in all of your calculations.
Force P=500 [kN]
Modulus of Elasticity E=200 [GPa] (same for both cables)
Lengths on beam : a=1.6 [m] ; b=0.8 [m]
Lengths of cables : L1 = 0.75 [m] ; L2 = 0.6 [m]
Cross-section cables : A1 = 1100 [mm2] ; A2 = 1300 [mm2]
Following Questions need to be answered:
Force @ Point A
Stress @ Point A
change in length of L1
Force @ Point C
Stress @ Point C
change in length of L2
angle formed by beam and horizontal
Support force B?
2)Both, a brass tube and the steel rod located inside the brass tube are solidly attached to common end plates A and B at either end.
The respective diameters are :
Do = 5.2 [cm]
Di = 3.0 [cm]
d= 2.9[cm]
Brass:
alpha=19x10^-6/degree celsius
E=210GPa
Steel:
alpha=12x10^-6/degree celsius
E=105GPa
Initially the assembly is stress free.
Now the temperature increases simultaneously for the brass tube and steel rod by 60oC. As a result the distance L between the two end plates will change.
Determine the resulting stresses in the brass tube and the steel rod, counting tension as positive and compression as negative.
Following Questions to be answered:
Stress in Brass in MPa
Stress in Steel in MPa
1) A rigid beam is supported at point B by a pin/hole connection and by two cables at points A and C, respectively.
Initially (before load P is applied), there is no slack nor tension in either of the two cables. Under influence of load "P" both cables will be under tension and the beam will have rotated slightly in counter-clockwise direction. Neglect the weight of the beam in all of your calculations.
Force P=500 [kN]
Modulus of Elasticity E=200 [GPa] (same for both cables)
Lengths on beam : a=1.6 [m] ; b=0.8 [m]
Lengths of cables : L1 = 0.75 [m] ; L2 = 0.6 [m]
Cross-section cables : A1 = 1100 [mm2] ; A2 = 1300 [mm2]
Following Questions need to be answered:
Force @ Point A
Stress @ Point A
change in length of L1
Force @ Point C
Stress @ Point C
change in length of L2
angle formed by beam and horizontal
Support force B?
2)Both, a brass tube and the steel rod located inside the brass tube are solidly attached to common end plates A and B at either end.
The respective diameters are :
Do = 5.2 [cm]
Di = 3.0 [cm]
d= 2.9[cm]
Brass:
alpha=19x10^-6/degree celsius
E=210GPa
Steel:
alpha=12x10^-6/degree celsius
E=105GPa
Initially the assembly is stress free.
Now the temperature increases simultaneously for the brass tube and steel rod by 60oC. As a result the distance L between the two end plates will change.
Determine the resulting stresses in the brass tube and the steel rod, counting tension as positive and compression as negative.
Following Questions to be answered:
Stress in Brass in MPa
Stress in Steel in MPa