me shear stress for a rectangular cross-s
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![**Question:**
What is the shear stress for a rectangular cross-section 4"X8" and V = 20kips?
**Answer Explanation:**
To calculate the shear stress (τ) for a given rectangular cross-section, we use the formula:
\[ \tau = \frac{V}{A} \]
where:
- \( \tau \) is the shear stress
- \( V \) is the applied shear force
- \( A \) is the area of the cross-section
In this problem:
- \( V \) is given as 20 kips (where 1 kip = 1000 pounds)
- The rectangular cross-section is 4 inches by 8 inches
First, we calculate the area (A) of the cross-section:
\[ A = \text{width} \times \text{height} = 4 \, \text{inches} \times 8 \, \text{inches} = 32 \, \text{square inches} \]
Next, we substitute the known values into the shear stress formula:
\[ \tau = \frac{V}{A} = \frac{20 \, \text{kips} \times 1000 \, \text{pounds/kip}}{32 \, \text{square inches}} = \frac{20000 \, \text{pounds}}{32 \, \text{square inches}} \approx 625 \, \text{psi} \]
Thus, the shear stress is approximately 625 psi.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50eb2229-1d0c-4dc7-966b-88adcd3ef11b%2F7dbb6879-6ebe-4d8c-823e-11a5704a8a7a%2Fwjfzomn_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
What is the shear stress for a rectangular cross-section 4"X8" and V = 20kips?
**Answer Explanation:**
To calculate the shear stress (τ) for a given rectangular cross-section, we use the formula:
\[ \tau = \frac{V}{A} \]
where:
- \( \tau \) is the shear stress
- \( V \) is the applied shear force
- \( A \) is the area of the cross-section
In this problem:
- \( V \) is given as 20 kips (where 1 kip = 1000 pounds)
- The rectangular cross-section is 4 inches by 8 inches
First, we calculate the area (A) of the cross-section:
\[ A = \text{width} \times \text{height} = 4 \, \text{inches} \times 8 \, \text{inches} = 32 \, \text{square inches} \]
Next, we substitute the known values into the shear stress formula:
\[ \tau = \frac{V}{A} = \frac{20 \, \text{kips} \times 1000 \, \text{pounds/kip}}{32 \, \text{square inches}} = \frac{20000 \, \text{pounds}}{32 \, \text{square inches}} \approx 625 \, \text{psi} \]
Thus, the shear stress is approximately 625 psi.
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