Math Problem Statement

E=210kN/mm²;I=150 000cm^4, l=2m,F1=70kN,F2=25kN,q=15kN/m

E=210kN/mm²; I=150,000 cm^4, l=2 m, F1=70 kN, F2=25 kN, q=15 kN/m. Use the principle of virtual forces (PvK) to calculate the deflection at points A and B of a beam subjected to these loads.

Solution

This image seems to be related to the calculation of deflections in a beam subjected to forces and a distributed load, using the principle of virtual forces (PvK). You are asked to calculate the deflection at points A and B for a beam under the action of forces F1F_1, F2F_2, and a uniformly distributed load qq.

The given values are:

  • E=210kN/mm2E = 210 \, \text{kN/mm}^2
  • I=150,000cm4I = 150,000 \, \text{cm}^4
  • l=2ml = 2 \, \text{m}
  • F1=70kNF_1 = 70 \, \text{kN}
  • F2=25kNF_2 = 25 \, \text{kN}
  • q=15kN/mq = 15 \, \text{kN/m}

You need to calculate the deflection at points A and B based on these values using the principle of virtual forces.

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Math Problem Analysis

Mathematical Concepts

Structural Mechanics
Deflection of Beams
Principle of Virtual Forces (PvK)

Formulas

PvK Formula: δ = ∫(M * M_virtual / (E * I)) dx
Bending Moment Equations for Distributed and Point Loads

Theorems

Principle of Virtual Work
Euler-Bernoulli Beam Theory

Suitable Grade Level

Undergraduate Engineering (Civil/Mechanical Engineering)