Answer:
the change in length of the elastic rod is 0.147 mm and the vertical displacement of the point b is 0.1911 mm.
Explanation:
As the complete question is not visible , the complete question along with the diagram is found online and is attached herewith.
Part a
Take moments at point A to calculate the tensile force on the steel
rod at point C
[tex]\sum M_A=0\\T_c*2.5-P(2.5+0.75)-q*2.5*2.5/2=0\\T_c*2.5-10(3.25)-5*3.125=0\\T_c=19.25 kN\\[/tex]
Calculate the change in length of the elastic rod
[tex]\Delta l=\dfrac{T_c*L}{A*E}\\\Delta l=\dfrac{19.25\times 10^3*0.75}{\pi/4\times 0.025^2*200\times 10^9}\\\Delta l=0.000147 m \approx 0.147 mm[/tex]
So the change in length of the elastic rod is 0.147 mm.
As by the relation of the similar angles the vertical displacement of the point B is given as
[tex]\Delta B=\Delta l\dfrac{AC+BC}{AC}[/tex]
Here AC=2.5 m
BC=0.75 m
Δl=0.147 mm so the value is as
[tex]\Delta B=\Delta l\dfrac{AC+BC}{AC}\\\Delta B=0.147 mm\dfrac{2.5+0.75}{2.5}\\\Delta B=0.147 mm\dfrac{3.25}{2.5}\\\Delta B=0.1911 mm[/tex]
So the vertical displacement of the point b is 0.1911 mm.
