Structural Engineering

Engineering Mechanics

Equilibrium, resultants, trusses and friction — the statics foundation for every structural analysis question.

PART 1

Topic Breakdown & Traps

The Engineering Principle

A body is in static equilibrium when the net force and net moment vanish:

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

. These three planar equations solve any statically determinate structure. In a pin-jointed truss, members carry only axial force; the method of joints applies

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

at each pin.

The Core Formula Matrix

Equilibrium (planar):

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

Resultant of two perpendicular forces:

R = F_{1}^{2} + F_{2}^{2}

Moment:

M = F \times d

(force × perpendicular distance)

Limiting friction:

F = μ N

Truss determinacy:

m + r = 2 j

(perfect truss),

m

=members,

r

=reactions,

j

=joints.

The ‘IIT Traps’

⚠
Perpendicular distance only. A moment uses the perpendicular distance from the pivot to the line of action — not the slant distance.
⚠
Zero-force members. Identify them first to simplify truss analysis; they still exist physically (stability).
⚠
Sign convention. Fix a consistent sense (e.g. CCW moment positive) before summing.

📚 Standard references

Mechanics of Structures — B.C. Punmia
Vector Mechanics for Engineers: Statics — Beer & Johnston

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · NAT

Two forces

6 kN

and

8 kN

act at right angles at a point. Their resultant is _____ kN.

Q2MEDIUM1 Mark · NAT

A simply supported beam of span

6 m

carries a UDL of

20 kN/m

. Each support reaction is _____ kN.

Q3HARD2 Marks · MCQ

A perfect plane truss has

7

joints. The number of members required is: