Page 32 - Handbook of Civil Engineering Calculations, Second Edition

STATICS, STRESS AND STRAIN, AND FLEXURAL ANALYSIS 1.15

FIGURE 8

2. Take moments with respect to an assumed point
Assume that the maximum tension of 1800 lb (8006 N) occurs in segment PR (Fig. 8).
The reaction at P, which is collinear with PR, is therefore 1800 lb (8006 N). Compute the
true perpendicular distance m from Q to PR by taking moments with respect to Q. Or
M Q 1800m 500(35) 750(17) 0; m 16.8 ft (5.1 m). This dimension establish-
es the true position of PR.
3. Start the graphical solution of the problem
In Fig. 8b, draw a circular arc having Q
as center and a radius of 16.8 ft (5.1 m). Draw a
line through P
tangent to this arc. Locate R
on this tangent at a horizontal distance of
15 ft (4.6 m) from P
.
4. Draw the force vectors
In Fig. 8c, draw vectors ab, bc, and cd to represent the 750-lb (3336-N) load, the 500-lb
(2224-N) load, and the 1800-lb (8006-N) reaction at P, respectively. Complete the trian-
gle by drawing vector da, which represents the reaction at Q.
5. Check the tension assumption
Scale da to ascertain whether it is less than 1800 lb (8006 N). This is found to be so, and
the assumption that the maximum tension exists in PR is validated.
6. Continue the construction
Draw a line through Q
in Fig. 8b parallel to da in Fig. 8c. Locate S
on this line at a hori-
zontal distance of 17 ft (5.2 m) from Q.
7. Complete the construction
Draw R
S
and db. Test the accuracy of the construction by determining whether these
lines are parallel.