Loaded Parallel to the Web

Oct 13, 2025 by leolavanderia.com.br 126 views

Introduction

In this example, we will determine the shear resistance of a UPE240 European steel rolled channel section with parallel flanges in grade S275 steel. The UPE240 channel section is a type of structural steel section commonly used in building construction and other engineering applications. The shear resistance of a channel section is an important parameter in designing structures that are subjected to shear forces.

Material Properties

The material properties of the UPE240 channel section are as follows:

Steel Grade: S275
Yield Strength (f_y): 275 N/mm^2
Ultimate Tensile Strength (f_u): 430 N/mm^2
Shear Yield Strength (f_vy): 159 N/mm^2
Shear Ultimate Tensile Strength (f_vu): 275 N/mm^2

Section Properties

The section properties of the UPE240 channel section are as follows:

Depth (d): 240 mm
Flange Width (b_f): 120 mm
Flange Thickness (t_f): 8 mm
Web Thickness (t_w): 5 mm
Moment of Inertia (I_y): 12300 mm^4
Moment of Inertia (I_z): 2400 mm^4
Section Modulus (Z_y): 4200 mm^3
Section Modulus (Z_z): 1200 mm^3

Loading Conditions

We will consider two loading conditions:

Loaded Parallel to the Web

In this loading condition, the shear force is applied parallel to the web of the channel section. The shear force is resisted by the web of the channel section.

Loaded Parallel to the Flange

In this loading condition, the shear force is applied parallel to the flange of the channel section. The shear force is resisted by the flange of the channel section.

Solution

Loaded Parallel to the Web

To determine the shear resistance of the channel section when loaded parallel to the web, we need to calculate the shear stress in the web.

The shear stress in the web can be calculated using the following formula:

τ = V / (A_w * f_vy)

where:

τ = shear stress in the web (N/mm^2)
V = shear force (N)
A_w = area of the web (mm^2)
f_vy = shear yield strength of the steel (N/mm^2)

The area of the web can be calculated using the following formula:

A_w = t_w * b_w

where:

A_w = area of the web (mm^2)
t_w = web thickness (mm)
b_w = web width (mm)

The web width can be calculated using the following formula:

b_w = d - 2 * t_f

where:

b_w = web width (mm)
d = depth of the channel section (mm)
t_f = flange thickness (mm)

Substituting the values, we get:

A_w = 5 mm * (240 mm - 2 * 8 mm) = 200 mm^2

Now, we can calculate the shear stress in the web:

τ = V / (A_w * f_vy) = V / (200 mm^2 * 159 N/mm^2)

The shear resistance of the channel section when loaded parallel to the web can be calculated using the following formula:

V = τ * A_w

Substituting the values, we get:

V = (V / (200 mm^2 * 159 N/mm^2)) * 200 mm^2 = V

Therefore, the shear resistance of the channel section when loaded parallel to the web is equal to the applied shear force.

Loaded Parallel to the Flange

To determine the shear resistance of the channel section when loaded parallel to the flange, we need to calculate the shear stress in the flange.

The shear stress in the flange can be calculated using the following formula:

τ = V / (A_f * f_vy)

where:

τ = shear stress in the flange (N/mm^2)
V = shear force (N)
A_f = area of the flange (mm^2)
f_vy = shear yield strength of the steel (N/mm^2)

The area of the flange can be calculated using the following formula:

A_f = t_f * b_f

where:

A_f = area of the flange (mm^2)
t_f = flange thickness (mm)
b_f = flange width (mm)

Substituting the values, we get:

A_f = 8 mm * 120 mm = 960 mm^2

Now, we can calculate the shear stress in the flange:

τ = V / (A_f * f_vy) = V / (960 mm^2 * 159 N/mm^2)

The shear resistance of the channel section when loaded parallel to the flange can be calculated using the following formula:

V = τ * A_f

Substituting the values, we get:

V = (V / (960 mm^2 * 159 N/mm^2)) * 960 mm^2 = V

Therefore, the shear resistance of the channel section when loaded parallel to the flange is equal to the applied shear force.

Conclusion

In this example, we have determined the shear resistance of a UPE240 European steel rolled channel section with parallel flanges in grade S275 steel. The shear resistance of the channel section is equal to the applied shear force when loaded parallel to the web or the flange. The shear stress in the web and the flange can be calculated using the formulas provided above.

Discussion

The shear resistance of a channel section is an important parameter in designing structures that are subjected to shear forces. The shear resistance of a channel section depends on the material properties, section properties, and loading conditions.

In this example, we have considered two loading conditions: loaded parallel to the web and loaded parallel to the flange. The shear resistance of the channel section is equal to the applied shear force in both loading conditions.

The shear stress in the web and the flange can be calculated using the formulas provided above. The shear stress in the web is higher than the shear stress in the flange due to the larger area of the web.

The shear resistance of a channel section can be increased by increasing the material properties, such as the yield strength and ultimate tensile strength, or by increasing the section properties, such as the moment of inertia and section modulus.

References

Eurocode 3: Design of steel structures. Part 1-1: General rules and rules for buildings. (2005)
British Standard BS 5950: 2000. Structural use of steelwork in building. Code of practice for design loads for buildings. (2000)
American Society of Civil Engineers (ASCE). (2010). Minimum design loads for buildings and other structures. ASCE/SEI 7-10.
Q&A: Determining the Shear Resistance of a UPE240 European Steel Rolled Channel Section =====================================================================================

Q: What is the shear resistance of a UPE240 European steel rolled channel section with parallel flanges in grade S275 steel?

A: The shear resistance of a UPE240 European steel rolled channel section with parallel flanges in grade S275 steel is equal to the applied shear force when loaded parallel to the web or the flange.

Q: How do you calculate the shear stress in the web of a UPE240 European steel rolled channel section?

A: The shear stress in the web of a UPE240 European steel rolled channel section can be calculated using the following formula:

τ = V / (A_w * f_vy)

where:

τ = shear stress in the web (N/mm^2)
V = shear force (N)
A_w = area of the web (mm^2)
f_vy = shear yield strength of the steel (N/mm^2)

Q: How do you calculate the area of the web of a UPE240 European steel rolled channel section?

A: The area of the web of a UPE240 European steel rolled channel section can be calculated using the following formula:

A_w = t_w * b_w

where:

A_w = area of the web (mm^2)
t_w = web thickness (mm)
b_w = web width (mm)

Q: How do you calculate the web width of a UPE240 European steel rolled channel section?

A: The web width of a UPE240 European steel rolled channel section can be calculated using the following formula:

b_w = d - 2 * t_f

where:

b_w = web width (mm)
d = depth of the channel section (mm)
t_f = flange thickness (mm)

Q: How do you calculate the shear stress in the flange of a UPE240 European steel rolled channel section?

A: The shear stress in the flange of a UPE240 European steel rolled channel section can be calculated using the following formula:

τ = V / (A_f * f_vy)

where:

τ = shear stress in the flange (N/mm^2)
V = shear force (N)
A_f = area of the flange (mm^2)
f_vy = shear yield strength of the steel (N/mm^2)

Q: How do you calculate the area of the flange of a UPE240 European steel rolled channel section?

A: The area of the flange of a UPE240 European steel rolled channel section can be calculated using the following formula:

A_f = t_f * b_f

where:

A_f = area of the flange (mm^2)
t_f = flange thickness (mm)
b_f = flange width (mm)

Q: What are the material properties of a UPE240 European steel rolled channel section with parallel flanges in grade S275 steel?

A: The material properties of a UPE240 European steel rolled channel section with parallel flanges in grade S275 steel are as follows:

Steel Grade: S275
Yield Strength (f_y): 275 N/mm^2
Ultimate Tensile Strength (f_u): 430 N/mm^2
Shear Yield Strength (f_vy): 159 N/mm^2
Shear Ultimate Tensile Strength (f_vu): 275 N/mm^2

Q: What are the section properties of a UPE240 European steel rolled channel section with parallel flanges?

A: The section properties of a UPE240 European steel rolled channel section with parallel flanges are as follows:

Depth (d): 240 mm
Flange Width (b_f): 120 mm
Flange Thickness (t_f): 8 mm
Web Thickness (t_w): 5 mm
Moment of Inertia (I_y): 12300 mm^4
Moment of Inertia (I_z): 2400 mm^4
Section Modulus (Z_y): 4200 mm^3
Section Modulus (Z_z): 1200 mm^3

Q: What are the loading conditions for determining the shear resistance of a UPE240 European steel rolled channel section?

A: The loading conditions for determining the shear resistance of a UPE240 European steel rolled channel section are as follows:

Loaded Parallel to the Web: The shear force is applied parallel to the web of the channel section.
Loaded Parallel to the Flange: The shear force is applied parallel to the flange of the channel section.

Q: How do you determine the shear resistance of a UPE240 European steel rolled channel section?

A: The shear resistance of a UPE240 European steel rolled channel section can be determined by calculating the shear stress in the web and the flange, and then using the formulas provided above to calculate the shear resistance.

Q: What are the references for determining the shear resistance of a UPE240 European steel rolled channel section?

A: The references for determining the shear resistance of a UPE240 European steel rolled channel section are as follows:

Eurocode 3: Design of steel structures. Part 1-1: General rules and rules for buildings. (2005)
British Standard BS 5950: 2000. Structural use of steelwork in building. Code of practice for design loads for buildings. (2000)
American Society of Civil Engineers (ASCE). (2010). Minimum design loads for buildings and other structures. ASCE/SEI 7-10.