### 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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Answered: 6-1.2-1 Find longest span for a timber…

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

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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