The basic differential equation of the elastic curve for a cantilever beam is given by the following ODE as: Given L = 120 inches; E = 30,000 ksi; I = 800 in4; P=1 kip Initial Condition: y(0) = 0 Solve numerically the ODE for beam deflection y(x) with ∆x = 20 inches, using Euler’s Method. Write the Euler’s equations for the first two nodes and show your computational work. You can use an Excel file for the rest.Tabulate the results and Plot (x,y).

The simply supported beam shown below carries its own weight, a uniformly distributed live load of 300 lbs/ft, and a concentrated dead load På at midspan. The cross-section of the beam is U- shaped. It has two rows of reinforcing bars at the bottom. The bottom row has five #6 bars and the top row has three #6 bars. Let ƒ' =4,000 psi and ƒ¸ = 60 ksi. The cross-sectional area of a #6 bar is 0.44 in.². W₁ = 300 lbs/ft 10 ft. PD * 10 ft. 17 in. 3 in. b 8 #6 bars + 00 6 in. 00 14 in. b + 9 in. State the difference between a tension-controlled beam and a compression-controlled beam in terms of the strain in the reinforcement in precise and succinct sentences. Why does ACI require that a beam has to be tension-controlled?

The part shown below is formed from 3-mm diameter steel wire with R = 40 cm. A force is applied with P of 10 Newtons. The modulus of elasticity of steel is 200 GPa. Use Castigliano's method to estimate the horizontal deflection at point C. 2R

Note:Hand written solution not allowed.