# Analyzing a Cantilever Beam with a Triangular Distributed Load### Problem StatementConsider a cantilever beam fixed at point A and subjected to a triangular distributed load with a maximum intensity of 7 kips per foot (7 k/f) over a length of 12 feet. The objectives are to:1. Draw the Shear and Moment Diagrams.2. Find the maximum values of shear force (Vmax) and bending moment (Mmax).### Given Data- Maximum load intensity, \( w = 7 \frac{\text{kips}}{\text{foot}} \)- Length of the beam, \( L = 12 \text{ feet} \)### Loading DetailsThe load is a triangular distributed load, which linearly decreases from 7 kips per foot at point A to 0 kips per foot at the free end.### Steps to Analyze1. **Support Reactions:** - As the beam is fixed at A, it provides reactions in the vertical and horizontal directions, and a moment.2. **Shear Diagram (V):** - For a triangular distributed load, the shear force will vary parabolically. - The maximum shear force will occur at the fixed end (point A).3. **Moment Diagram (M):** - The moment diagram will be cubic due to the triangular load. - Maximum moment occurs at the fixed point.### Shear Force CalculationUsing the property of a triangular load, the equivalent point load \( P \) acts at \( \frac{1}{3} \) the distance from the larger end (which is at the fixed support).\[P = \frac{1}{2} \cdot w_{max} \cdot L = \frac{1}{2} \cdot 7 \cdot 12 = 42 \text{ kips}\]The resultant point load acts at:\[x = \frac{1}{3} \cdot 12 = 4 \text{ feet}\]So, the reaction at the fixed end A is:\[V_A = P = 42 \text{ kips}\]### Moment CalculationThe maximum moment at the fixed end:\[M_A = P \cdot x = 42 \cdot 4 = 168 \text{ kip-feet}\]### Shear and Moment Di

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Answered: 7k/f 12' Draw Shear & Moment Diagrams.…

Engineering

Civil Engineering

7k/f 12' Draw Shear & Moment Diagrams. Find Vmax, V=0, Mmax, M=0

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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