6-1.2-1 Find longest span for a timber 12x2 carrying a load of 1200#/ft with FV: 175psi, Fb = 1750 E = 1,700,000psi NOMINAL SIZE b d A Sx lx 12X24 11.25 23.00 258.75 991.88 11,406.56
6-1.2-1 Find longest span for a timber 12x2 carrying a load of 1200#/ft with FV: 175psi, Fb = 1750 E = 1,700,000psi NOMINAL SIZE b d A Sx lx 12X24 11.25 23.00 258.75 991.88 11,406.56
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Example Problem: Calculating the Longest Span for a Timber Beam
**Problem Statement:**
Determine the longest span for a timber beam with a nominal size of 12 inches by 24 inches (12X24) that carries a load of 1200 pounds per foot (1200 #/ft). Use the following material properties:
- Shear stress (\( F_v \)) = 175 psi
- Bending stress (\( F_b \)) = 1750 psi
- Modulus of Elasticity (\( E \)) = 1,700,000 psi
**Cross-Sectional Properties:**
Below is a table detailing the dimensions and structural properties of the timber beam:
| NOMINAL SIZE | b (in) | d (in) | A (in²) | Sx (in³) | Ix (in⁴) |
|--------------|--------|--------|----------|----------|------------|
| 12X24 | 11.25 | 23.00 | 258.75 | 991.88 | 11,406.56 |
**Table Explanation:**
- **NOMINAL SIZE**: Refers to the specified dimensions of the timber beam in inches.
- **b**: Actual width of the timber beam in inches.
- **d**: Actual depth of the timber beam in inches.
- **A**: Cross-sectional area in square inches.
- **Sx**: Section modulus in cubic inches, which is a geometric property that indicates the strength of a cross-section to resist bending.
- **Ix**: Moment of inertia in fourth power of inches (in⁴), which measures the beam's resistance to deformation under loading.
**Step-by-Step Solution:**
1. **Determine the maximum allowable shear force (V_max):**
\[
V_{\text{max}} = F_v \times A
\]
\[
V_{\text{max}} = 175 \, \text{psi} \times 258.75 \, \text{in}^2 = 45,281.25 \, \text{lb}
\]
2. **Calculate the uniformly distributed load (w) allowed by the shear force:**
\[
w = \frac{2 \times V_{\text{max}}}{L}
\]
Given:
\[
w =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50eb2229-1d0c-4dc7-966b-88adcd3ef11b%2Fbe01bb7e-685a-49fc-962a-3d73a4fd033e%2Fnr3qm3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Problem: Calculating the Longest Span for a Timber Beam
**Problem Statement:**
Determine the longest span for a timber beam with a nominal size of 12 inches by 24 inches (12X24) that carries a load of 1200 pounds per foot (1200 #/ft). Use the following material properties:
- Shear stress (\( F_v \)) = 175 psi
- Bending stress (\( F_b \)) = 1750 psi
- Modulus of Elasticity (\( E \)) = 1,700,000 psi
**Cross-Sectional Properties:**
Below is a table detailing the dimensions and structural properties of the timber beam:
| NOMINAL SIZE | b (in) | d (in) | A (in²) | Sx (in³) | Ix (in⁴) |
|--------------|--------|--------|----------|----------|------------|
| 12X24 | 11.25 | 23.00 | 258.75 | 991.88 | 11,406.56 |
**Table Explanation:**
- **NOMINAL SIZE**: Refers to the specified dimensions of the timber beam in inches.
- **b**: Actual width of the timber beam in inches.
- **d**: Actual depth of the timber beam in inches.
- **A**: Cross-sectional area in square inches.
- **Sx**: Section modulus in cubic inches, which is a geometric property that indicates the strength of a cross-section to resist bending.
- **Ix**: Moment of inertia in fourth power of inches (in⁴), which measures the beam's resistance to deformation under loading.
**Step-by-Step Solution:**
1. **Determine the maximum allowable shear force (V_max):**
\[
V_{\text{max}} = F_v \times A
\]
\[
V_{\text{max}} = 175 \, \text{psi} \times 258.75 \, \text{in}^2 = 45,281.25 \, \text{lb}
\]
2. **Calculate the uniformly distributed load (w) allowed by the shear force:**
\[
w = \frac{2 \times V_{\text{max}}}{L}
\]
Given:
\[
w =
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