A truss is a structure made of members joined at their ends. For the truss shown

Question

A truss is a structure made of members joined at their ends. For the truss shown in the figure, the forces in the nine members are determined by solving the following system of nine equations: F^2+cos(48.81^.)F1, - 0 F^6 + cos(48.81^.)F^2 - o. -sin(48.81)F^3 + F^3 - 0 - cos(48.81^.)F^1 + F^4 - 0 -sin(48.81^.)F^1 + F^3 - 1800, - F^4 - cos(48.81^.)F^5 = 1200, -F^7 - sin(48.81)F^5 - sin(45^.)F9 = 0, sin(45^.)F9 = 1500, -cos(45^.)F9 - F^2 = 0 Write the equations in matrix from and use MATLAB to determine the forces in the members. A positive force means tensile force and a negative force means compressive force. Display the results in a table where the first column displays the member number and the second column displays the corresponding force.

Explanation / Answer

Equation (1) is wrong. The horizontal sum of forces at hinge 1 is = hor. force exerted by the hinge (which we do not know).

Consider a vertical force Fv1 (upwards) at hinge 1 (joining trusses 1 and 2), and a vertical force Fv2 (upwards) at hinge 2 (joining trusses 6, 7 and 8). The sum of torques about hinge 2 is 0:

Fv1*84 + 1800*42 + 1200*48 = 1500*42 => Fv1 = 835.7 N

The sum of torques about hinge 1 is 0:

1200*48 = 1800*42 + 1500*126 + Fv2*84 => Fv2 = 2464.3 N

Thus, F7 = -Fv2 = -2464.3 N.

F9 = 1500/sin(45) = 2121.3 N (from eqn 8 given).

-F1*sin(48.81) = Fv1 => F1 = -1110.5 N.

F4 = F1*cos(48.81) = -731.3 N.

F3 = (-F7-sin(45)*F9)/sin(48.81) = 1281.4 N

F5 = -F3/sin(48.81) = -1702.8 N

F8 = -cos(45)*F9 = 1500 N

F6 - F2 = -cos(48.81)*F5 = 1121.4 N.

F6 and F2 are not determinable here. They are between the 2 hinges.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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