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When vertical intermediate stiffeners are subjected to bending moments due to eccentricity of vertical loads, their moment of inertia (cm4) is increased by
Where,
M = the applied bending moment kN-m
D = overall depth of girder in mm
E = Young’s modulus in MPa
t = thickness of web, mm
Where,
M = the applied bending moment kN-m
D = overall depth of girder in mm
E = Young’s modulus in MPa
t = thickness of web, mm
- a)125MD2/Et
- b)150MD2/Et
- c)175MD2/Et
- d)225MD2/Et
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
When vertical intermediate stiffeners are subjected to bending moments...
's modulus of the material in GPa
t = thickness of the stiffener in mm
y = distance from the neutral axis to the centroid of the stiffener in mm
The moment of inertia (I) of the stiffener can be calculated using the parallel axis theorem:
I_stiffener = I_stiffener' + A_stiffener * y^2
Where:
I_stiffener' = moment of inertia of the stiffener about its own centroid (cm^4)
A_stiffener = area of the stiffener (cm^2)
The moment of inertia of the stiffener about its own centroid can be calculated using the following formula:
I_stiffener' = (t * D^3) / 12
The area of the stiffener can be calculated by multiplying its thickness (t) by the depth of the girder (D), minus twice the distance from the neutral axis to the centroid of the stiffener (2y):
A_stiffener = t * (D - 2y)
Substituting the values of I_stiffener' and A_stiffener into the equation for I_stiffener:
I_stiffener = (t * D^3) / 12 + t * (D - 2y) * y^2
When the stiffener is subjected to bending moments due to eccentricity of vertical loads, the moment of inertia (I_stiffener) is increased.
t = thickness of the stiffener in mm
y = distance from the neutral axis to the centroid of the stiffener in mm
The moment of inertia (I) of the stiffener can be calculated using the parallel axis theorem:
I_stiffener = I_stiffener' + A_stiffener * y^2
Where:
I_stiffener' = moment of inertia of the stiffener about its own centroid (cm^4)
A_stiffener = area of the stiffener (cm^2)
The moment of inertia of the stiffener about its own centroid can be calculated using the following formula:
I_stiffener' = (t * D^3) / 12
The area of the stiffener can be calculated by multiplying its thickness (t) by the depth of the girder (D), minus twice the distance from the neutral axis to the centroid of the stiffener (2y):
A_stiffener = t * (D - 2y)
Substituting the values of I_stiffener' and A_stiffener into the equation for I_stiffener:
I_stiffener = (t * D^3) / 12 + t * (D - 2y) * y^2
When the stiffener is subjected to bending moments due to eccentricity of vertical loads, the moment of inertia (I_stiffener) is increased.
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Community Answer
When vertical intermediate stiffeners are subjected to bending moments...
The moment of inertia (I) of a vertical intermediate stiffener is increased by the formula:
ΔI = (M * D^2) / (4 * E)
Where:
ΔI = increase in moment of inertia (cm^4)
M = applied bending moment (kN-m)
D = overall depth of girder (mm)
E = Young's modulus (N/mm^2)
This formula accounts for the increase in moment of inertia due to the eccentricity of vertical loads.
ΔI = (M * D^2) / (4 * E)
Where:
ΔI = increase in moment of inertia (cm^4)
M = applied bending moment (kN-m)
D = overall depth of girder (mm)
E = Young's modulus (N/mm^2)
This formula accounts for the increase in moment of inertia due to the eccentricity of vertical loads.
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When vertical intermediate stiffeners are subjected to bending moments due to eccentricity of vertical loads, their moment of inertia (cm4) is increased byWhere,M = the applied bending moment kN-mD = overall depth of girder in mmE = Young’s modulus in MPat = thickness of web, mma)125MD2/Etb)150MD2/Etc)175MD2/Etd)225MD2/EtCorrect answer is option 'B'. Can you explain this answer?
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