(o) Isometric view of spoce truss (b) View normol to yz planeFIGURE 11- Compute the true length of each member
Use the equation d = (d% + d* + dz^2 )^0 5 , where d = the true length of a member. - Compute the ratio of the projected length to the true length
For each member, compute the ratios of the three projected lengths to the true length. For
example, for member AC, dzld = 6/12.04 = 0.498.
These ratios are termed direction cosines because each represents the cosine of the an-
gle between the member and the designated axis, or an axis parallel thereto.
Since the axial force in each member has the same direction as the member itself, a di-
rection cosine also represents the ratio of the component of a force along the designated
axis to the total force in the member. For instance, let AC denote the force in member AC,
and let ACx denote its component along the x axis. ThQnACxIAC = dx/d = 0.249. - Determine the component forces
Consider joint A as a free body, and assume that the forces in the three truss members are
TABLE 3 Data for Space Truss (Fig. 11)
Member AB AC AD
4,ft(m) 3 (0.91) 3 (0.91) 10 (3.03)
4,ft(m) 10 (3.0) 10 (3.0) 10 (3.0)
4,ft(m) 4 (1.2). 6 (1.8) O (O)
</,ft(m) 11.18 (3.4) 12.04 (3.7) 14.14 (4.3)
dxld 0.268 0.249 0.707
dyld 0.894 0.831 0.707
djd 0.358 0.498 O
Force, Ib (N) -3830 (-17,036) -2750 (-12,232) +8080 (+35,940)