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 7 members are determined by solving the following system of 7 equations. F_1 cos 28.5 degree + F_2 = 3000, F_1 sin 28.5 degree = -6521, -F_1 cos 28.5 degree - F_3 cos 58.4 degree + F_5 cos 58.4 degree + F_6 cos 28.5 degree = -3000, -F_1 sin 28.5 degree - F_3 sin 58.4 degree - F_5 sin 58.4 degree - F_6 sin 28.5 degree = 0, -F_4 -F_5 cos 58.4 degree +F_7 = 0, F_6 sin 28.5 degree = -7479, F_6 cos 28.5 degree + F_7 = 0. By inspection, this system is uncoupled in F_1 and F_6 and by substitution, 3 other forces can be determined and the system is reduced to 2 equations in unknown forces. Solve this system by hand and compare your results with that obtained from MATLAB.

Explanation / Answer

b) From eqn(2)

F1=-6521/sin28.50= -13666 lb

From eqn (6)

F6= -7479/sin28.50 =-15674 lb

From eqn (2)

F2=3000-(-13666)cos28.50= 15010 lb

From eqn (7)

F7= -(-15674)cos28.50= 13774 lb

From eqn (3)

-(-13666)cos28.50-F3cos58.40+F5cos58.40+(-15674)cos28.50=-3000

Or

-F3+F5= -2358 lb----(a)

From eqn (4)

-(-13666)sin28.50-F3sin58.40-F5sin58.40-(-15674)sin28.50=0

F3+F5=16437----(b)

Adding eqns (a) and (b)

2F5= 14079

F5= 7039.5 lb

From (b)

F3= 16437-7039.5 = 9397.5 lb

From eqn (5)

F4=F7-F5cos58.40= 13774-7039.5cos58.40= 10086 lb

Hence

F1= -13666 lb

F2=15010 lb

F3= 9397.5 lb

F4= 10086 lb

F5= 7039.5 lb

F6= -15674 lb

F7= 13774 lb

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