CELE Engineering Mechanics — Frames, Machines and CablesConcept Map

Concept

Frames

Sub Concepts

• Multi-force members (loaded at ≥3 points or carrying moments)
• Two-force members (identify to reduce unknowns)
• Pin connections (Newton's third law — equal and opposite)
• Dismembering method (FBD of each member separately)
• External reactions (from whole frame FBD first)
• Internal pin forces (member-to-member interactions)
• Equilibrium equations (ΣFx = 0, ΣFy = 0, ΣM = 0 per member)

Relationship To Central

Stationary structures with multi-force members; analyzed by dismembering and applying equilibrium

Concept

Machines

Sub Concepts

• Input force (effort)
• Output force (load/resistance)
• Mechanical advantage (M.A. = load/effort)
• Effort arm vs load arm
• Lever principle (M.A. = effort arm / load arm)
• Pin-jointed linkages
• Dismembering and equilibrium (same as frames)
• Force multiplication or displacement advantage

Relationship To Central

Moving/articulated structures that transmit or modify forces; analyzed like frames but with input–output force relationship focus

Concept

Cables

Sub Concepts

• Tension only (no compression or bending)
• Concentrated loads → funicular polygon (straight segments)
• Uniform horizontal load → parabolic shape
• Self-weight along cable length → catenary shape
• Horizontal component H (constant throughout cable)
• Vertical component (varies with slope angle)
• Maximum tension at steepest point (supports)
• Sag-to-span ratio (determines shape and tension distribution)
• Cable geometry relationships

Relationship To Central

Perfectly flexible members carrying only tension; shape determined by load type

Concept

Equilibrium Principles

Sub Concepts

• Force equilibrium (ΣFx = 0, ΣFy = 0)
• Moment equilibrium (ΣM = 0 about any point)
• Free body diagrams (FBD)
• Newton's third law (action–reaction at pins)
• Two-force member condition (force along member)
• Three-force member condition (forces concurrent or parallel)

Relationship To Central

Foundation for analyzing all three types; applies to rigid bodies in static equilibrium

Concept

Load Types and Shapes

Sub Concepts

• Concentrated point loads
• Distributed loads (uniform, triangular, etc.)
• Horizontal load distribution (suspension bridges)
• Load along cable length (self-weight)
• Funicular polygon (concentrated load cable)
• Parabolic cable equation
• Catenary equation (advanced)

Relationship To Central

Determines how cables deform and how forces distribute in structures

Concept

Key Formulas and Relationships

Sub Concepts

• Mechanical advantage: M.A. = F_load / F_effort
• Lever M.A.: M.A. = L_effort / L_load
• Parabolic cable: H = wL² / 8d
• Max tension in parabolic cable: T_max = √[H² + (wL/2)²]
• Cable tension at angle: T = H / cos(θ)
• Funicular cable: H = constant, T = H / cos(θ) per segment
• Moment equilibrium: ΣM = 0

Relationship To Central

Quantitative tools for solving frames, machines, and cables

Concept

Analysis Methods

Sub Concepts

• Dismembering technique (frames/machines)
• Section method (for internal forces)
• Method of joints vs method of members
• Graphical funicular polygon
• Analytical resolution (angles and components)
• Step-by-step equilibrium application

Relationship To Central

Systematic procedures for solving structure problems

Concept

Common Exam Mistakes

Sub Concepts

• Treating multi-force members as two-force members
• Forgetting Newton's third law at pins
• Confusing cable shapes (parabola vs catenary)
• Placing max tension at midspan instead of supports
• Incorrect sign convention in equilibrium equations
• Not identifying two-force members first
• Errors in FBD orientation and direction

Relationship To Central

Pitfalls to avoid in PRC Civil Engineer Licensure Exam

To

Equilibrium Principles

From

Frames

Strength

strong

Relationship

Frames are solved by applying equilibrium equations (ΣF = 0, ΣM = 0) to each dismembered member.

To

Two-Force Members

From

Frames

Strength

strong

Relationship

Identifying two-force members in a frame immediately specifies force direction, simplifying equilibrium analysis.

To

Frames

From

Machines

Strength

strong

Relationship

Machines are analyzed using the same dismembering and equilibrium methods as frames, but focus on input–output force relationship.

To

Mechanical Advantage

From

Machines

Strength

strong

Relationship

Machines are defined by their ability to change force magnitude and direction; M.A. quantifies this benefit.

To

Tension Only

From

Cables

Strength

strong

Relationship

Cables, being perfectly flexible, can only carry tension; this fundamental property determines analysis methods.

To

Load Types and Shapes

From

Cables

Strength

strong

Relationship

The shape of a cable (parabola, catenary, or funicular polygon) is determined by the type of load applied.

To

Cables

From

Key Formulas and Relationships

Strength

strong

Relationship

Parabolic cable formula H = wL²/8d and T_max = √[H² + (wL/2)²] are essential tools for cable problems.

To

Machines

From

Key Formulas and Relationships

Strength

strong

Relationship

Mechanical advantage formulas (M.A. = F_load/F_effort, M.A. = L_effort/L_load) directly solve machine problems.

To

Analysis Methods

From

Equilibrium Principles

Strength

strong

Relationship

All analysis methods—dismembering, section method, funicular polygon—are grounded in equilibrium principles.

To

Analysis Methods

From

Frames

Strength

strong

Relationship

Frames use the dismembering technique: draw FBD of whole structure, then each individual member, and apply equilibrium systematically.

To

Equilibrium Principles

From

Cables

Strength

moderate

Relationship

Cable tension is found by applying force equilibrium (ΣF = 0) at load points and using the constant horizontal component.

To

Frames

From

Common Exam Mistakes

Strength

moderate

Relationship

Common pitfall: treating multi-force members as two-force members, leading to incorrect results.

To

Cables

From

Common Exam Mistakes

Strength

moderate

Relationship

Common pitfall: confusing parabolic cable (uniform horizontal load) with catenary (self-weight), or placing max tension at midspan instead of supports.

To

Equilibrium Principles

From

Two-Force Members

Strength

moderate

Relationship

Two-force member condition (force along member) is a direct consequence of moment equilibrium about each end.

To

Equilibrium Principles

From

Mechanical Advantage

Strength

moderate

Relationship

M.A. relationships are derived from moment equilibrium at the machine's pivot(s): Fe × Le = FL × la.