A hypothetical truss comprising of weightless members is shown in the following Figure. Assuming tension to be positive and compression to be negative, the value of force in member TU (in kN, rounded off to one decimal place) is ___________.
Step 1: Geometry and Loads
Span:
$VT = 4 \text{ m}$
$TS = 4 \text{ m}$
Height:
$UW = 3 \text{ m}$
Loads:
At $W$: $40 \text{ kN}$ (horizontal)
At $U$: $30 \text{ kN}$ (vertical downward)
Supports:
$V$ → pin
$S$ → roller
Step 2: Global Equilibrium
Take moments about $V$:
$8R_S - 30(4) - 40(3) = 0$
$8R_S - 120 - 120 = 0$
$8R_S = 240$
$R_S = 30 \text{ kN}$
Vertical equilibrium:
$R_V + 30 - 30 = 0$
$R_V = 0$
Horizontal equilibrium:
$H_V = 40 \text{ kN}$
Step 3: Joint T
At joint $T$, members meeting:
$VT$, $TS$, and $TU$
There is no external load at T.
Since $R_V = 0$, member $VT$ carries no vertical force.
Thus at joint $T$:
Only possible vertical force is in member $TU$.
For equilibrium:
$F_{TU} = 0$
Final Answer
$\boxed{0.0 \text{ kN}}$
(Member TU is a zero-force member.)
Important Questions from Design of Structural Elements
A simply supported RCC beam of span 4 m is supporting a brick wall over its entire span. The brick wall is 250 mm thick and 2 m high. The RCC beam has a depth of 600 mm and width of 250 mm. The density of brick masonry and RCC can be assumed as 18 KN/m³ and 25 KN/m³ respectively. Considering the load of the wall and self-weight of the RCC beam, the maximum bending moment in the beam (in KN-m) will be ____________ [rounded off to two decimal places].
A simply supported beam having effective span of 5 meter is carrying a centrally concentrated load of 16 kN. The maximum bending moment in the beam in kN-m is _______________
Area of tensile steel per meter width of a reinforced concrete slab is 335 sq mm. If 8 mm rods are used as reinforcement, then centre to centre spacing of the reinforcement in mm is _______________
- The maximum bending moment ($kNm$) in a simply supported beam of 8 $m$ span subjected to a uniformly distributed load of 20 $kN/m$ (inclusive of its self-weight) over the entire span is
- Which of the following is NOT a mechanism of bond resistance in reinforced concrete?
