For the beam shown in the following Figure, assuming a sagging moment (generating tensile stresses at the bottom fibre) as positive and a hogging moment (generating tensile stresses at the top fibre) as negative, the bending moment (in kN.m, rounded off to one decimal place) at section X-X is ___________.
Step 1: Geometry and Loads
Span:
$W \to X = 2 \text{ m}$
$X \to Y = 2 \text{ m}$
$Y \to Z = 1 \text{ m}$
Total span $W \to Y = 4 \text{ m}$
UDL:
$w = 20 \text{ kN/m}$ over $4 \text{ m}$
Point load:
$120 \text{ kN}$ at $Z$
Step 2: Replace UDL with equivalent load
Total UDL load:
$W = 20 \times 4 = 80 \text{ kN}$
Acts at midpoint of 4 m span:
$2 \text{ m}$ from $W$
Step 3: Support reactions
Take moments about $W$:
$R_Y(4) - 80(2) - 120(5) = 0$
$4R_Y - 160 - 600 = 0$
$4R_Y = 760$
$R_Y = 190 \text{ kN}$
Vertical equilibrium:
$R_W + 190 - 80 - 120 = 0$
$R_W = 10 \text{ kN}$
Step 4: Bending moment at section X (2 m from W)
Consider left portion.
Moment at $X$:
$M_X = R_W(2) - w \dfrac{(2)^2}{2}$
$M_X = 10(2) - 20 \times \dfrac{4}{2}$
$M_X = 20 - 40$
$M_X = -20 \text{ kN-m}$
Final Answer
$\boxed{-20.0 \text{ kN-m}}$
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?
