The axial force F_t in each of the 13 member pin-connected truss, shown in the f

Question

The axial force F_t in each of the 13 member pin-connected truss, shown in the figure, can be calculated by solving the following system of 13 equations: F_2 + 0.7071 F_1 = 0, -F_2 + F_6 = 0, F_3 - 2000 = 0 F_4 + 0.6585 F_5 - 0.7071F_1 = 0 0.7071F_1 + F_3 + 0.7526F_5 + 1000 = 0 F_7 + 0.6585 F_8 - F_4 = 0, 0.7526F_8 + F_9 + 500 = 0 F_10 - 0.6585 F_5 - F_6 = 0, F_9 + 0.7526 F_5 - 4000 = 0 0.7071F_11 - F_7 = 0, 0.7071F_11 + F_12 + 500 = 0 F_12 + 0.7526 F_8 - 2000 = 0, F_13 + 0.7071F_11 = 0 Solve the previous equations for the axial forces.

Explanation / Answer

The given equations to be solved are :

1. 0.7071F1 + F2 = 0
2. -F2 + F6 = 0
3. F3 - 2000 = 0
4. -0.7071F1 + F4 + 0.6585F5 + 1000 = 0
5. 0.7071F1 + F3 + 0.7256F5 + 1000 = 0
6. -F4 + F7 + 0.6585F8 = 0
7. 0.7526F8 + F9 + 500 = 0
8. -0.6585F5 - F6 + F10 = 0
9. 0.7526F5 + F9 - 4000 = 0
10. -F7 + 0.7071F11 = 0
11. 0.7071F11 + F12 + 500 = 0
12. 0.7526F8 + F12 - 2000 = 0
13. 0.7071F11 + F13 = 0

solving the 13 system of 13 equations for 13 variables, we cam make a matrix
{aik} {Fj} = {kik}
where aik are constnat coefficients of Fj from the equatioons awith kik being the constants in these equations
this system can be solved with cramers rule for |{aik}| ! = 0

solving we get
F1 = -6789.5 N
F2 = 4800 N
F3 = 2000 N
F4 = -7435.17 N
F5 = 2481.8 N
F6 = 4800.85 N
F7 = -5132.14 N
F8 = -3497.39 N
F9 = 2132.14 N
F10 = 6435.17 N
F11 = -7258.01 N
F12 = 4632.14 N
F13 = 5132.14 N

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.