Geomechanics & Ground Control

Engineering Mechanics

Free-body diagrams, equilibrium, moments and friction — the statics toolkit underpinning every support, pillar and equipment-loading calculation.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Engineering mechanics (statics) analyses bodies in equilibrium. A body is in equilibrium when the net force and net moment are zero:

\sum F_{x} = 0

\sum F_{y} = 0

\sum M = 0

. The first step is always a free-body diagram (FBD) isolating the body and showing every external force (loads, reactions, friction, weight). A moment measures a force's turning effect about a point:

M = F \times d

, where

d

is the perpendicular distance from the pivot to the line of action. Dry friction resists impending sliding up to a limit

F = μ N

(coefficient of friction

μ

× normal reaction

N

); on an incline of angle

θ

, sliding impends when

tan θ = μ

The Core Formula Matrix

Force equilibrium:

\sum F_{x} = 0, \sum F_{y} = 0

Moment equilibrium:

\sum M = 0

, with

M = F d_{⊥}

Limiting friction:

F_{ma x} = μ N

Angle of repose (block on incline): sliding impends when

tan θ = μ

, i.e.

θ = tan^{- 1} μ

The ‘IIT Traps’

⚠
Moment uses the perpendicular distance to the line of action, not the slant distance to the point of application.
⚠
**Friction is $μ N$ , and $N$ is not always $m g$ .** On an incline $N = m g cos θ$ ; applied vertical forces also change $N$ .
⚠
Friction opposes *impending* motion and is $\leq μ N$ when static; only at the verge of sliding does $F = μ N$ .
⚠
Take moments about an unknown's line of action to eliminate it — choosing the pivot wisely halves the algebra.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

The moment of a force about a point is the product of the force and the:

Q2MEDIUM2 Marks · NAT

A block rests on a rough horizontal surface with coefficient of friction

0.30

and normal reaction

500 N

. The maximum static friction force available is ______ N. (Round to the nearest whole number.)

Q3HARD2 Marks · NAT

A uniform horizontal beam of length

4 m

is simply supported at both ends and carries a single vertical point load of

600 N

1 m

from the left support. The vertical reaction at the left support is ______ N. (Round to the nearest whole number.)