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A beam of I section 600mm deep and 200 mm wide has flanges 25 mm thick and web 20 mm thick. If the shear stress in the web at the junction of flange and web is q, then the shear stress in the flange at the junction is?
Most Upvoted Answer
A beam of I section 600mm deep and 200 mm wide has flanges 25 mm thick...
Solution:
Given:
Depth of the section, d = 600 mm
Width of the section, b = 200 mm
Thickness of the flange, tf = 25 mm
Thickness of the web, tw = 20 mm
Shear stress in the web, q = ?
To find: Shear stress in the flange at the junction.
Assumptions:
1. The section is symmetric about the y-axis.
2. The section is subjected to pure bending.
3. The distribution of the shear stress is linear across the depth of the section.
Calculation:
1. Calculation of the shear force in the section:
The shear force, V at the section can be calculated using the formula:
V = (w x L)/2
Where,
w = load per unit length
L = span of the beam
As the load on the beam is not given, let's assume a uniformly distributed load of 10 kN/m.
L = 1 m (Assuming a simply supported beam)
V = (10 x 1)/2 = 5 kN
2. Calculation of the shear stress in the web:
The maximum shear stress in the web occurs at the junction of the web and flange.
Shear stress in the web, q = (V x tw)/(b x tf)
q = (5 x 1000 x 20)/(200 x 25) = 40 N/mm^2
3. Calculation of the shear stress in the flange:
The distribution of the shear stress is linear across the depth of the section. Hence, the shear stress in the flange can be calculated using the following formula:
Shear stress in the flange, σf = (q x (d/2 - tf))/((d/2))
σf = (40 x (600/2 - 25))/(600/2) = 30 N/mm^2
Answer:
Hence, the shear stress in the flange at the junction is 30 N/mm^2.
Given:
Depth of the section, d = 600 mm
Width of the section, b = 200 mm
Thickness of the flange, tf = 25 mm
Thickness of the web, tw = 20 mm
Shear stress in the web, q = ?
To find: Shear stress in the flange at the junction.
Assumptions:
1. The section is symmetric about the y-axis.
2. The section is subjected to pure bending.
3. The distribution of the shear stress is linear across the depth of the section.
Calculation:
1. Calculation of the shear force in the section:
The shear force, V at the section can be calculated using the formula:
V = (w x L)/2
Where,
w = load per unit length
L = span of the beam
As the load on the beam is not given, let's assume a uniformly distributed load of 10 kN/m.
L = 1 m (Assuming a simply supported beam)
V = (10 x 1)/2 = 5 kN
2. Calculation of the shear stress in the web:
The maximum shear stress in the web occurs at the junction of the web and flange.
Shear stress in the web, q = (V x tw)/(b x tf)
q = (5 x 1000 x 20)/(200 x 25) = 40 N/mm^2
3. Calculation of the shear stress in the flange:
The distribution of the shear stress is linear across the depth of the section. Hence, the shear stress in the flange can be calculated using the following formula:
Shear stress in the flange, σf = (q x (d/2 - tf))/((d/2))
σf = (40 x (600/2 - 25))/(600/2) = 30 N/mm^2
Answer:
Hence, the shear stress in the flange at the junction is 30 N/mm^2.
Community Answer
A beam of I section 600mm deep and 200 mm wide has flanges 25 mm thick...
T=(VQ)/Ib, T(shear stress) is indirectly proportional to b.
so T2/T1=b2/b1
T2=(b2/b1)×T1
where b2=width of web, b1= width of flange
given T1=q
T2=(20/200)×q
=0.1q
so T2/T1=b2/b1
T2=(b2/b1)×T1
where b2=width of web, b1= width of flange
given T1=q
T2=(20/200)×q
=0.1q
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A beam of I section 600mm deep and 200 mm wide has flanges 25 mm thick and web 20 mm thick. If the shear stress in the web at the junction of flange and web is q, then the shear stress in the flange at the junction is?
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A beam of I section 600mm deep and 200 mm wide has flanges 25 mm thick and web 20 mm thick. If the shear stress in the web at the junction of flange and web is q, then the shear stress in the flange at the junction is? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A beam of I section 600mm deep and 200 mm wide has flanges 25 mm thick and web 20 mm thick. If the shear stress in the web at the junction of flange and web is q, then the shear stress in the flange at the junction is? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam of I section 600mm deep and 200 mm wide has flanges 25 mm thick and web 20 mm thick. If the shear stress in the web at the junction of flange and web is q, then the shear stress in the flange at the junction is?.
A beam of I section 600mm deep and 200 mm wide has flanges 25 mm thick and web 20 mm thick. If the shear stress in the web at the junction of flange and web is q, then the shear stress in the flange at the junction is? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A beam of I section 600mm deep and 200 mm wide has flanges 25 mm thick and web 20 mm thick. If the shear stress in the web at the junction of flange and web is q, then the shear stress in the flange at the junction is? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam of I section 600mm deep and 200 mm wide has flanges 25 mm thick and web 20 mm thick. If the shear stress in the web at the junction of flange and web is q, then the shear stress in the flange at the junction is?.
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