Math Problem Statement
Given Data: Beam type: W18x50 Material: A36 steel Fy (Yield strength): 248 MPa Loads: Point load: 10 kN at 2m from left support Point load: 15 kN at 4m from left support Point load: 10 kN at 8m from left support Uniformly Distributed Load (UDL): 40 kN/m over 6m span (from 2m to 8m)
Solution
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Math Problem Analysis
Mathematical Concepts
Statics
Structural Analysis
Beam Deflection
Equilibrium Equations
Shear Force and Bending Moment Diagrams
Formulas
Sum of Vertical Forces: ΣFy = 0
Sum of Moments: ΣMA = 0
Bending Stress: σ = M*c/I
Shear Force at a Section: V = ΣFy to the left or right of the section
Theorems
Equilibrium of Forces and Moments
Flexural Formula for Beam Bending
Suitable Grade Level
Undergraduate Engineering
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