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
- The slenderness ratio of a circular column of diameter $300 \text{ mm}$ and effective height $3 \text{ m}$ is _________ [in integer]
- Match the structural system in Group I with their potential causes of failure in Group II
Group I Group II (P) Flat Slab (1) Thrust (Q) Long Column (2) Flutter (R) Arch (3) Punching Shear (S) Tensile Fabric (4) Buckling (5) Moment A basement wall resists lateral pressure exerted by soil and water. The soil pressure amounts to $4.5 \text{ kN/m}^2$ for every metre of depth below Ground Level (GL). The sub-soil water level is $1.0 \text{ m}$ below GL and hydrostatic pressure of water is $9.8 \text{ kN/m}^2$ for every metre of depth below GL. The total lateral pressure (in $kN/m^2$, rounded off to one decimal place) exerted on the wall $2 \text{ m}$ below GL is______
- Slenderness ratio of a column is represented as:
For a symmetrical two dimensional truss as shown in the above figure, vertical force in kN acting on the member PQ is ________
