Item 4 Determine the displacement of A The A709 steel rod is

Item 4 Determine the displacement of A The A709 steel rod is subjected to the loading shown with P-8 kN. (Figure 1) The cross- sectional area of the rod is 80 mm4, Neglect the size of the couplings at B and C Express your answer to three significant figures and include appropriate units 3.15 mm vious Answers All attempts used; correct answer displayed Figure 1 of 1> Part B 0.75 m Determine the displacement of B 45 45° Express your answer to three significant figures and include appropriate units 1.50 m 6 KN 6 KN 2.58mm 5 kN 5 kN Submit Previous Answers Request Answe Incorrect: Try Again; 4 attempts remaining

Solution

Axial load in part AB=P=8 kN=8000 N

Axial load in part BC = 8+2*6*sin45=16485.28 N

Axial load in part CD=16.48+2*6*sin45=24970.56 N

Modulus of elasticity of A709 steel = 200 GPa=2*10⁵ N/mm²

area of cross section=80 mm²

Stress in part AB=8000/80=100 N/mm²

Stress in part BC=16485.28/80=206.066 N/mm²

Stress in part CD=24970.56/80=312.132 N/mm²

length of CD=0.75 m=750 mm

length of BC=1.5 m = 1500 mm

length of AB=1 m = 1000 mm

Strain in AB=100/2*10⁵ = 0.0005

Strain in BC=206.066/2*10⁵=0.00103

Strain in CD=312.132/2*10⁵ = 0.00156

displacement of C with respect to D=0.00156*750=1.17 mm

displacement of B with respect to C = 0.00103*1500=1.545 mm

displacement of A with respect to B=0.0005*1000=0.5 mm

total displacement of A=1.17+1.545+0.5=3.215 mm

total displacement of B=1.17+1.545=2.715 mm