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# Figure P-2-13.6 Figưre P-2-13.7 Figure P-2.13.9 Figure P-2-13.11 Figure P-2-13.13 RESLLTANTS OF FORCE STSTENS 2-13.8. Determine the amount and position of the resultant of the loads acting on the Fink truss shown in Fig. P-2-13.8. $R=3.500 \mathrm{lb} \text { down at } 12 \mathrm{ft} \text { to right of } A$ Figure P-2-13.8 Ans. 2-13.9. Find the values of $P$ and $F$ so that the four forces shown in Fig. P-2-13.9 produce an upward resultant of $300 \mathrm{lb}$ acting at $4 \mathrm{ft}$ from the left end of the bar. 2-13.10. A beam of length $L$ supports a load which varies uniformly from $w \mathrm{lb} / \mathrm{ft}$ at the right end to zero at the left end. Show that the resultant load is $W=w L / 2$ acting at $L / 3$ from the right end. 2-13.11. The beam $A B$ in Fig. P-2-13.11 supports a load which varies uniformly from an intensity of $60 \mathrm{lb} / \mathrm{ft}$ to $180 \mathrm{lb} / \mathrm{ft}$. Calculate the magnitude and position of the resultant load. Hint: Replace the given loading by two equivalent triangular loadings each similar to the loading of Prob. 2-13.10. 2-13.12. The 16 -ft wing of a small airplane is subjected to a lift which varies from zero at the tip to $360 \mathrm{lb} / \mathrm{ft}$ at the fuselage according to $w=90 x^{1 / 2}$ where $x$ is measured in feet from the tip. Compute the resultant lift and its location from the wing tip. $R=3840 \mathrm{lb} \text { at } 9.60 \mathrm{ft}$ Ans. 2-13.13. Compute the resultant of the three forces acting on the plate shown in Fig. P-2-13.13. Locate its intersection with $A B$ and $B C$. $R=776 \mathrm{lb} \text { down to the right at } \theta_{A}=40.6^{\circ}$ $\text { acting } 3.43 \text { in. above } B \text { and } 4 \text { in. right of } B$ Ans. 2-13.14. Determine the resultant of the three forces acting on the dam shown in Fig. P-2-13.14 and locate its intersection with the base $A B$. For good design, this intersection should occur within the middle third of the base. Does it? Yes Ans. 2-13.15. The Howe rooftruss shown in Fig. P-2-13.15 carries the given loads. The wind loads are perpendicular to the inclined members. Determine the resultant and its intersection with $A B$. 2.13 Resultant of Any Force System 71 Figure P-2-13.14 Figure P-2-13.15 2-13.16. The three forces shown on the grid in Fig. P-2-13.16 produce a horizontal resultant force through point $A$. Find the magnitude and sense of $P$ and $F$. 2-13.17. The resultant of four forces, of which three are shown in Fig. P-2-13.16, is $390 \mathrm{lb}$ acting down to the right with a slope of 5 to 12 through point $A$. If $P=150 \mathrm{lb}$ and $F=130 \mathrm{lb}$, determine the missing force $T$ and its $x$ intercept. $T=180.5 \text { acting down to the right at } \theta_{h}=33.7^{\circ}$ $\text { located } 3.1 \mathrm{ft} \text { to right of } O$ Ans. 2-13.18. The three forces shown in Fig. P-2-13.18 are required to cause a horizontal resultant acting through point $A$. If $T=316 \mathrm{lb}$, determine the values of $P$ and $F$. $P=-180.5 \mathrm{lb} ; F=336 \mathrm{lb}$ Ans. 2-13.19. The three forces in Fig. P-2-13.18 create a vertical resultant acting through point $B$. If $P=361 \mathrm{lb}$, compute the values of $T$ and $F$. 2-13.20. The rectangular block of Fig. P-2-13.20 is acted upon by a set of forces whose force multipliers and directions are as follows: $P_{m}=$ $20 \mathrm{lb} / \mathrm{ft}$ directed from $A$ to $E, Q_{m}=10 \mathrm{lb} / \mathrm{ft}$ directed from $B$ to $C, T_{m}=$ Figure P.2-13.16 Figure P-2-13.18 Figure P-2-13.20 answer 2.13.11, 2.13.13, 2.13.16, 2.13.17  