Problem Solving: Show your solution.
1. The figure shows a rigid bar that is supported by a
pin at A and two rods, one made of steel and the
other of bronze. Neglecting the weight of the bar,
compute the stress in each rod caused by the
50-kN load, the following data:
Steel
1.0 m
Bronze
2 m
А
Steel
600
200
Bronze
300
83
toomk
Area (mm)
E (GPa)
1.0 m-e
40.8 m
50 KN
st
1
R
0.8 m
A,
0.6 m
1.0 m
HINT: Apply this equation in step 1 to get
Pst and Pbr.
MA = 0+1
0.6Pst + 1.6Pbr = 2.4(50x103)
Ах
50 KN
(b) FBD
0.6 m
1.0 m
0.8 m
A-
ANSWERS: Ost = 191.8 MPa; Obr = 106.1 MPa
Ost
dor
oncrete column has
diameter of 300
The
Answers
Answer:
Problem Solving: Show your solution.
1. The figure shows a rigid bar that is supported by a
pin at A and two rods, one made of steel and the
other of bronze. Neglecting the weight of the bar,
compute the stress in each rod caused by the
50-kN load, the following data:
Steel
1.0 m
Bronze
2 m
А
Steel
600
200
Bronze
300
83
toomk
Area (mm)
E (GPa)
1.0 m-e
40.8 m
50 KN
st
1
R
0.8 m
A,
0.6 m
1.0 m
HINT: Apply this equation in step 1 to get
Pst and Pbr.
MA = 0+1
0.6Pst + 1.6Pbr = 2.4(50x103)
Ах
50 KN
(b) FBD
0.6 m
1.0 m
0.8 m
A-
ANSWERS: Ost = 191.8 MPa; Obr = 106.1 MPa
Ost
dor
oncrete column has
diameter of 300
The
To calculate the stress in each rod caused by the 50-kN load, we need to determine the force in each rod and then divide by the cross-sectional area.
Step 1: Calculate the force in each rod.
We can use the equation of equilibrium to find the force in each rod.
F_steel + F_bronze = Load
where F_steel is the force in the steel rod, F_bronze is the force in the bronze rod, and Load is the applied load of 50 kN.
Since the bar is supported by a pin at A, we know that the moment at A is zero, which means that the clockwise moment created by the steel rod must be equal to the counterclockwise moment created by the bronze rod.
0.6F_steel x 0.8 + 1.6F_bronze x 1.0 = 2.4 x Load
Solving for F_steel and F_bronze:
0.6F_steel = 1.6 x Load - 1.6F_bronze
F_steel = 2.67 x Load - 2.67F_bronze
Substituting the value of Load (50 kN) into the above equation:
F_steel = 134 kN - 2.67F_bronze
And
F_bronze = (134 - F_steel) / 2.67
Step 2: Calculate the stress in each rod.
The stress in each rod can be calculated using the formula:
Stress = Force / Area
Where Force is the force calculated in step 1, and Area is the cross-sectional area of each rod.
For the steel rod:
Stress_steel = F_steel / Area_steel
For the bronze rod:
Stress_bronze = F_bronze / Area_bronze
Substituting the values for Force and Area:
Stress_steel = (134 - 2.67F_bronze) / 600 mm^2 = 191.8 MPa
Stress_bronze = F_bronze / 300 mm^2 = 106.1 MPa
Therefore, the stress in the steel rod is 191.8 MPa, and the stress in the bronze rod is 106.1 MPa.
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