According to the general shear stress formua, shear stress distribution on a rectangular crosss section is parabolic. When b = 47 mm, h = 79 mm, transverse shear force V = 69 k N, please calculate the max shear stress on the cross section shown below: max (f v max in textbook)= ____ MPa.
According to the general shear stress formua, shear stress distribution on a rectangular crosss section is parabolic. When b = 47 mm, h = 79 mm, transverse shear force V = 69 k N, please calculate the max shear stress on the cross section shown below: max (f v max in textbook)= ____ MPa.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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According to the general shear stress formua, shear stress distribution on a rectangular crosss section is parabolic. When b = 47 mm, h = 79 mm, transverse shear force V = 69 k N, please calculate the max shear stress on the cross section shown below: max (f v max in textbook)= ____ MPa.
![**Shear Stress Distribution in Rectangular Cross Sections**
**Theory and Calculation:**
According to the general shear stress formula, the shear stress distribution on a rectangular cross-section is parabolic. For the given dimensions and transverse force, calculate the maximum shear stress.
**Parameters:**
- Breadth (\(b\)) = 47 mm
- Height (\(h\)) = 79 mm
- Transverse shear force (\(V\)) = 69 kN
**Objective:**
Calculate the maximum shear stress (\(\tau_{\text{max}}\)) on the cross-section.
**Formula:**
\[
\tau_{\text{max}} = \frac{3V}{2bh}
\]
**Diagram Explanation:**
The diagram displays a rectangle oriented such that the shorter side (breadth, \(b\)) aligns with the horizontal \(z\)-axis, and the longer side (height, \(h\)) aligns with the vertical \(y\)-axis. Arrows indicate the axes on the left side of the rectangle.
**Calculations:**
Insert your calculated value:
\[
\tau_{\text{max}} = \left(\frac{3 \times 69,000 \, \text{N}}{2 \times 47 \, \text{mm} \times 79 \, \text{mm}} \right) = \, \_\_\_\_ \, \text{MPa}
\]
Make sure to convert mm to meters if necessary for the calculations and fill in the blank with the computed maximum shear stress value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35813974-6b68-4217-bd4c-21bf1a217db1%2F13aad236-bcf1-4dbb-9e62-0330e5ec1587%2Ffqsdvhz_processed.png&w=3840&q=75)
Transcribed Image Text:**Shear Stress Distribution in Rectangular Cross Sections**
**Theory and Calculation:**
According to the general shear stress formula, the shear stress distribution on a rectangular cross-section is parabolic. For the given dimensions and transverse force, calculate the maximum shear stress.
**Parameters:**
- Breadth (\(b\)) = 47 mm
- Height (\(h\)) = 79 mm
- Transverse shear force (\(V\)) = 69 kN
**Objective:**
Calculate the maximum shear stress (\(\tau_{\text{max}}\)) on the cross-section.
**Formula:**
\[
\tau_{\text{max}} = \frac{3V}{2bh}
\]
**Diagram Explanation:**
The diagram displays a rectangle oriented such that the shorter side (breadth, \(b\)) aligns with the horizontal \(z\)-axis, and the longer side (height, \(h\)) aligns with the vertical \(y\)-axis. Arrows indicate the axes on the left side of the rectangle.
**Calculations:**
Insert your calculated value:
\[
\tau_{\text{max}} = \left(\frac{3 \times 69,000 \, \text{N}}{2 \times 47 \, \text{mm} \times 79 \, \text{mm}} \right) = \, \_\_\_\_ \, \text{MPa}
\]
Make sure to convert mm to meters if necessary for the calculations and fill in the blank with the computed maximum shear stress value.
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