Question

Given: Consider the truss shown below with the loading on joints B and C. Find: Use the method of joints to determine the load carried by each member in the truss. Identify each member as either being in tension, in compression or carrying zero load. Leave your answers in terms of P. For this problem, use the following parameters: h = 0.8 m and b = 0.6 m. h X B C b b Р Р

Answer 1

Ans

FBD

Vo D HD h 04 HA x A B C b b P Р

01 = tan tan 0.8 0.6 53.13° b

$\theta_2 = tan^{-1}\frac{h}{2b}=tan^{-1}\frac{0.8}{2*0.6}=33.69 ^o$

Consider joint C

TDC 04 TBC C P

Using Lami's theorem, we get

Toc TBC P sin 90 sin (270 – 12 sin02

$\Rightarrow \frac{T_{DC}}{sin90}=\frac{T_{BC}}{sin(270-33.69)}=\frac{P}{sin33.69}$

$\Rightarrow \frac{T_{DC}}{sin90}=\frac{T_{BC}}{sin(236.31)}=\frac{P}{sin33.69}$

$\therefore T_{DC} = \frac{Psin90}{sin33.69}=1.8P$ (Tensile)

and, $T_{BC} = \frac{Psin236.31}{sin33.69}=-1.5P$ (Compressive)

Consider joint B

Тов ө TAB Твс B P

  $\sum F_y = 0$

  $\Rightarrow T_{DB}sin\theta_1 =P$

  $\Rightarrow T_{DB}sin53.13 =P$

  $\Rightarrow T_{DB} =1.25P$ (tensile)

  $\sum F_x = 0$

$\Rightarrow -T_{AB}-T_{DB}cos\theta_1 + T_{BC} = 0$

$\Rightarrow -T_{AB}-1.25Pcos53.13 -1.5P = 0$

$\Rightarrow T_{AB} =-2.25P$ (compressive)

Consider joint A

TAD ТАВ НА А

  $\sum F_y = 0$

  $\Rightarrow T_{AD} =0$