Question

Learning Goal:

"bowstring truss" is often used in bridges as well as arched roofs.

Consider the following bowstring truss:
Forces: P₁= 5.5 kip   P₂ =8.5 kip      P₃ = 15 kip      P₄ =20 kip
Dimensions:   b = 3 ft     h₁ = 2 ft   h₂ = 0.9 ft     h₃ = 0.4 ft  

P. P. hi

Determine the forces in all the members of the truss and state if each is in tension or compression. Please note the symmetry of the truss.

Express your answers to three significant figures and include the appropriate units. You must show all work including all free body diagrams and all intermediate calculations.

You MUST include an summary answer table that includes all of the member forces and if they are tension or compression. The table shall look like the following:

Answer 1

8.S 8.5 8.S oY FH 8.5 о. 9 fr. 5.5 5.5 20 IS" IST R g R. 3 fh 3fH

Using the condihion equiibrium Total pA farces Toral Down wert dor ces. Fs om the diagram, it is cler that the rus is Loaded mm ot mically 2 ㅋ R8^ 51.PS, kips. RF = 51.75 kips. At toint A: AL 5.5 2- 3 AB 2. Sino, 31625 Sum vertical forces z 0 3.605

As the above obtained valu els positive directi ơnf Fat Shown İmathe FBD us correct AL Compressive foe Arrow away fromgeint → Tensile force] FAL 9.914 kips ( Tensile A A B AB 3.6os FAP8.2s kips. 8.25 kips (compressive) FAB BL A ton B: Вс A B 2 ヂ! FB L = 51-7S" kį PS (Compressive pre.ssive

の TAB 8.25 kips Camp-ressive) | Feen KL e- CL AL B L O .9 2. ~ FAL χ SI.ne,叶FBL_TkLx S1n92. sim2 3.132 KL3.131 3 132- Siam Layh

L3132 CL 3.605 3.6os の rCL = 8.25- FKL3 8lo kips 5 oips CL FcL kips Ten sile CK C D BC 20 2. 50 vessive

3 F333 ip As tha obtined value is negahive, dire.chion CD orrow sen før сь should be away from the Fc 33 359ip C Tensile 8.5 FHI 2 e. KL. DK 2.9 SJn": → 4.rt 2. ces e3 3. 02 4,172-

x Sin SL. 2.9 34 . 81 3:13. 4 3439 3 132 FX 33 313 kJ KJ 66 vips. C Tensile D K 8 S At tont Fks 1 J PJ

IT F85 3804 3.027 3.02T F1555 i ps. . F 1.555 kips CTensite Now as he Loadina i symmetrical, mem ber on the right halt oion of the russ have the same force as that dlina me m ber on the lett halt DJ For eram ple: ans membey AL ar Me mbes Corre spondin me mbens Similasly other me m ber forces can be abhaines or hon