For the beam shown below, ignoring the self-weight, the maximum hogging moment (in kN·m) generated for the loads indicated is_____________ (rounded off to one decimal place).
Step 1: Understand support conditions
Left end = pin support
Roller support is 2 m from start of UDL
There is an overhang of 2 m on the right
Hogging moment will occur at the roller support due to the 5 kN load on overhang
Step 2: Convert UDL into point load
UDL = $2 \text{ kN/m}$ over $2 \text{ m}$
Equivalent point load:
$W = 2 \times 2 = 4 \text{ kN}$
This acts at the center of the 2 m length.
Step 3: Find reactions
Let reactions be $R_A$ (left) and $R_B$ (roller).
Total downward load:
$3 + 4 + 5 = 12 \text{ kN}$
So,
$R_A + R_B = 12$
Taking moment about left support:
$R_B(4.5) = 3(1) + 4(3.5) + 5(6.5)$
$R_B(4.5) = 3 + 14 + 32.5$
$R_B(4.5) = 49.5$
$R_B = 11 \text{ kN}$
Then,
$R_A = 12 - 11 = 1 \text{ kN}$
Step 4: Maximum hogging moment
Maximum hogging occurs at roller support due to overhang load.
Taking moment at roller support:
$M_B = -5 \times 2$
$M_B = -10 \text{ kN-m}$
Maximum hogging moment (magnitude):
$\boxed{10.0 \text{ kN-m}}$
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 ________
