CELE Engineering Mechanics — Analysis of TrussesMemory Anchors
Mnemonics for Analysis of Trusses in the CELE 2026. Every one of these anchors has been designed to help you recall the concept under the pressure of Professional Regulation Commission (PRC) — Board of Civil Engineering's CELE Engineering Mechanics exam conditions.
Exam context
For the Civil Engineer Licensure Examination, Professional Regulation Commission (PRC) — Board of Civil Engineering tests Engineering Mechanics under a "Core" label, with Analysis of Trusses in the 3rd slot across 8 chapters. CELE candidates must clear the 70% weighted average, no sub-test below 50% cut on the 2026 paper, which draws about a meaningful share of Engineering Mechanics questions. Date to watch: May and November 2026.
Analysis of Trusses - Memory Anchors
Memory anchors transform abstract structural concepts into vivid mental images that your brain refuses to forget. Research in cognitive science shows that emotionally charged, story-linked, or absurdly visual cues are retained up to 6× longer than plain text repetition. For truss analysis — a perennial favorite in the PRC CE Board Exam — these anchors will let you reconstruct formulas, recall procedures, and spot zero-force members under exam pressure without hesitation. Work through each anchor at least twice, close your eyes to re-visualize, then test yourself with the recall trigger. The goal is not mere recognition but instant, effortless retrieval.
Anchors
Tags
- formula
- definition
- determinacy
Topic
Determinacy
Concept
Truss Determinacy Formula: m + r = 2j
Anchor Id
A1
Difficulty
easy
Memory Aid
MR. TWO JOINTS — 'MR' stands for Members + Reactions, and they must equal TWO times the Joints. Picture a strict examiner named 'Mr. 2J' checking every truss: if your truss can't satisfy Mr. 2J, it either collapses (unstable) or is over-constrained (indeterminate). Mr. 2J always demands exactly: m + r = 2j.
Anchor Type
mnemonic
Why It Works
The personification of the formula as 'Mr. 2J' creates a social-emotional hook. Anthropomorphizing equations dramatically increases recall because the brain's social cognition is highly activated.
Example Usage
Board question: A truss has 9 members, 3 reaction components, and 6 joints. Is it determinate? Recall Mr. 2J: m + r = 9 + 3 = 12, 2j = 2×6 = 12. Mr. 2J is satisfied — statically determinate!
Recall Trigger
Think of 'Mr. 2J' whenever you see a truss and need to check if it can be solved.
Tags
- definition
- analogy
- two-force member
Topic
Truss Assumptions
Concept
Truss members are two-force members carrying only axial force
Anchor Id
A2
Difficulty
easy
Memory Aid
A truss member is like a TAHO STICK — the bamboo stick of a taho vendor's container. It only carries the weight (axial force) of the taho pushing or pulling along its length. It cannot bend or twist the stick sideways because both ends are simply resting on pins (the vendor's hands at the joints). No moment, no shear — pure tension or compression along the stick.
Anchor Type
analogy
Why It Works
Culturally resonant Filipino imagery (taho vendor) makes the abstract concept of a two-force member immediately tangible for Filipino reviewees.
Example Usage
When asked why truss members carry no moment: remember the taho stick. Loads act at joints (the vendor's hands), so the stick is a pure axial member.
Recall Trigger
Taho stick — push or pull only, no bending.
Tags
- definition
- sequence
- acronym
Topic
Truss Assumptions
Concept
Three Truss Assumptions (Frictionless pins, Loads at joints only, Straight weightless members)
Anchor Id
A3
Difficulty
easy
Memory Aid
FLS — 'Frictionless, Loads-at-joints, Straight.' Say it as 'Feel Less Stress' when you remember truss assumptions. A truss FEELS LESS STRESS because: F = Frictionless pin connections (no moment transfer), L = Loads act at joints only (no midspan loading), S = Straight and weightless members. If all three hold, every member is a perfect two-force member.
Anchor Type
acronym
Why It Works
Acronym FLS converts three separate items into one retrievable word. The phrase 'Feel Less Stress' ties it emotionally to the benefit of simplified analysis — a self-referential memory hook.
Example Usage
Exam asks: What are the three assumptions in truss analysis? Recall FLS — Frictionless pins, Loads at joints, Straight members.
Recall Trigger
FLS → Feel Less Stress → Frictionless, Loads at joints, Straight members.
Tags
- definition
- sign convention
- visual
Topic
Method of Joints
Concept
Tension vs. Compression sign convention (assume tension positive)
Anchor Id
A4
Difficulty
easy
Memory Aid
Imagine two jeepneys parked bumper-to-bumper. A member in TENSION is like a passenger PULLING both jeepneys toward each other — the force arrows on the member point AWAY from the joint (the member stretches). A member in COMPRESSION is like a loaded truck PUSHING the jeepneys apart — force arrows point INTO the joint (the member squishes). Assume all members are tensile (passengers pulling). If the answer is negative, flip to compression (truck pushing).
Anchor Type
visual_association
Why It Works
Directional force visualization with culturally familiar vehicles anchors an abstract sign convention to a concrete spatial image.
Example Usage
After computing F_AC = −15.63 kN: the minus sign means compression — the jeepney truck is pushing. Annotate as C.
Recall Trigger
Jeepneys: pulling apart = tension (+), pushing together = compression (−).
Tags
- process
- sequence
- method of joints
Topic
Method of Joints
Concept
Method of Joints — start where only TWO unknown members exist
Anchor Id
A5
Difficulty
medium
Memory Aid
Imagine you are a detective (Engineer Dela Cruz) solving a crime at a truss construction site. You cannot interrogate a room with MORE than 2 suspects at once — you only have 2 equilibrium equations (ΣFx = 0, ΣFy = 0). So Detective Dela Cruz's golden rule: ALWAYS enter the joint where only 2 unknowns remain. Start at the support joint (where reactions are known), solve those 2 unknowns, then move like a chain reaction to the next joint — carrying your solved values like evidence.
Anchor Type
micro_story
Why It Works
Narrative structure (detective story) creates episodic memory. The two-equations-two-unknowns constraint is linked to the detective's 'can only interrogate 2 suspects' rule — a perfect isomorphism.
Example Usage
When starting method of joints: scan all joints, identify the one with only 2 unknowns. That is your entry point — just like Detective Dela Cruz picking his first room.
Recall Trigger
Detective Dela Cruz: never enter a joint with more than 2 unknown members.
Tags
- process
- method of sections
- formula
Topic
Method of Sections
Concept
Method of Sections — cut at most THREE members
Anchor Id
A6
Difficulty
medium
Memory Aid
The Method of Sections is like cutting a LUMPIA (spring roll) in half at a party. You can only slice through AT MOST 3 filling layers at once; if you try to cut through 4 unknown layers, the lumpia falls apart (you cannot solve it). Slice through exactly 3 members, take one half of the lumpia as your free body, and apply equilibrium. The best trick: take moments about the point where TWO of the cut members cross — only one unknown survives!
Anchor Type
analogy
Why It Works
The lumpia analogy creates a physical, sensory memory. The 'crossing point' trick is tied to the idea of eliminating two unknowns at once — exactly what happens when moments are taken at their intersection.
Example Usage
Need force in top chord EF: cut through EF, diagonal EC, and bottom chord BC (3 members). Take moments about point C (where EC and BC intersect) — only F_EF remains!
Recall Trigger
Cutting lumpia: 3 layers max, take moments at the crossing point.
Tags
- definition
- process
- zero-force
Topic
Zero-Force Members
Concept
Zero-Force Member Rule 1: Joint with two non-collinear members and NO load → both are zero-force
Anchor Id
A7
Difficulty
medium
Memory Aid
Picture a dead-end street corner (a T-intersection with NO traffic and NO street sign load). Two roads meet at the corner but NEITHER road goes anywhere and there is no load. Both roads carry ZERO traffic (zero force). If no one is pushing or pulling at that joint and the two members point in different directions, they both just sit there doing nothing.
Anchor Type
visual_association
Why It Works
Spatial visualization of an empty intersection is immediately retrievable. The 'no traffic, no force' analogy maps force to traffic flow.
Example Usage
Spot a joint with only 2 members (no load). Are they non-collinear? Yes → both are zero-force. Cross them out immediately to simplify the truss.
Recall Trigger
Dead-end corner with no traffic = two zero-force members.
Tags
- definition
- process
- zero-force
Topic
Zero-Force Members
Concept
Zero-Force Member Rule 2: Joint with three members (two collinear) and NO load → the odd member is zero-force
Anchor Id
A8
Difficulty
medium
Memory Aid
Three employees walk into a straight hallway (two members collinear along the hall). One employee is the ODD ONE OUT — he stands perpendicular off to the side (the third non-collinear member). The boss never gave him any work that day (no external load at the joint). So the odd employee does NOTHING — he is the zero-force member. The two hallway employees continue passing work between themselves along the chord.
Anchor Type
micro_story
Why It Works
The odd-one-out social dynamic is a culturally universal experience in Filipino offices. It creates an emotional peg for the third member being the zero-force one.
Example Usage
Vertical web member at a bottom-chord joint (two collinear bottom chords + one vertical, no load at joint) → vertical is zero-force. Skip it in your analysis.
Recall Trigger
Odd employee standing sideways with no work = zero-force member.
Tags
- sequence
- process
- method of joints
Topic
Method of Joints
Concept
Method of Joints procedure sequence
Anchor Id
A9
Difficulty
medium
Memory Aid
RAISE — Remember this 5-step sequence: R = find Reactions (whole truss equilibrium first), A = Assume all members in Tension, I = Identify starting joint (only 2 unknowns), S = Solve ΣFx=0 and ΣFy=0, E = Extend to adjacent joints. A CE reviewer who uses RAISE never forgets to compute reactions first — the #1 board exam pitfall.
Anchor Type
acronym
Why It Works
RAISE is a meaningful English word with strong recall. The 5 steps map naturally to the letters, and the pitfall warning reinforces emotional salience.
Example Usage
Before solving any joint problem: mentally say RAISE. Start with R (reactions), then A, I, S, E. This prevents forgetting reactions — the most common mistake.
Recall Trigger
RAISE your hand if you want to solve joints correctly.
Tags
- definition
- determinacy
- stability
Topic
Determinacy
Concept
Geometric instability despite m + r = 2j being satisfied
Anchor Id
A10
Difficulty
hard
Memory Aid
Passing the formula check (m + r = 2j) is like passing the paper requirements for a PRC application. But just because your papers are complete does NOT mean you are competent — you still need to actually be a real engineer (proper geometry). A truss with all concurrent or collinear members can have the right count of m, r, j but still collapse like a poorly arranged bamboo puzzle. The formula is necessary but NOT sufficient.
Anchor Type
analogy
Why It Works
The PRC application analogy is deeply relatable to CE board reviewees and creates an emotional anchor for the often-overlooked geometric instability condition.
Example Usage
Even if m + r = 2j, check that members are not all concurrent or collinear. A geometrically unstable truss will collapse regardless.
Recall Trigger
PRC paper requirements: necessary but not sufficient — same as m + r = 2j.
Tags
- definition
- conceptual
- zero-force
Topic
Zero-Force Members
Concept
Why zero-force members are NOT useless (buckling bracing and alternate load cases)
Anchor Id
A11
Difficulty
medium
Memory Aid
Imagine a barangay tanod (community guard) who has nothing to report tonight (zero-force under current loading). You might think he is useless — but remove him and a thief shows up tomorrow (different load case) or the neighboring guard leans on a wall and it buckles (buckling bracing). The tanod is still essential to the system's integrity. Zero-force members: apparently idle, secretly indispensable.
Anchor Type
micro_story
Why It Works
The barangay tanod analogy is uniquely Filipino and creates a sympathetic emotional connection to the concept. It also correctly captures both reasons (alternate loads + buckling prevention) in one story.
Example Usage
Exam question: Can you remove zero-force members from a truss? Answer: No — they prevent buckling of adjacent members and carry forces under alternate loading conditions.
Recall Trigger
Barangay tanod: zero activity tonight, but irreplaceable tomorrow.
Tags
- conceptual
- sign convention
- chord forces
Topic
Method of Sections
Concept
Top chord of a simply supported truss → compression; Bottom chord → tension
Anchor Id
A12
Difficulty
easy
Memory Aid
Imagine a simply supported wooden plank (bridge truss) with a load in the middle. The TOP surface SQUEEZES together (compression) like your face squinting in the sun. The BOTTOM surface STRETCHES apart (tension) like a smile. Top = squint = compression (C). Bottom = smile = tension (T). This is universal for simply supported beams and parallel-chord trusses under gravity loads.
Anchor Type
analogy
Why It Works
The facial expression analogy maps a structural concept to a visceral body experience — one of the most powerful forms of embodied memory.
Example Usage
Before solving Example 2 top chord EF: predict answer will be negative (compression). Compute F_EF = −16 kN — confirms the squinting face analogy.
Recall Trigger
Top chord = squinting face (C); Bottom chord = smiling face (T).
Tags
- formula
- process
- method of sections
- rhyme
Topic
Method of Sections
Concept
Method of Sections: take moments about intersection of the other two cut members
Anchor Id
A13
Difficulty
medium
Memory Aid
When the section cut is done, and three unknowns there are — Pick the point where TWO of them meet, and you'll go far. Take your moment right at that spot, the other two disappear. One equation, one unknown — the answer becomes clear!
Anchor Type
rhyme
Why It Works
Rhyming structures engage the brain's phonological loop and are among the most ancient and effective memory devices. The rhyme encapsulates the core technique of moment selection in Method of Sections.
Example Usage
Finding F_EF: the two other cut members are EC and BC. They meet at C. Take moments about C → F_EF appears alone in the equation.
Recall Trigger
Sing the rhyme: 'Pick the point where TWO of them meet...'
Tags
- definition
- determinacy
- stability
Topic
Determinacy
Concept
Instability condition: m + r < 2j means the truss is a mechanism (unstable)
Anchor Id
A14
Difficulty
easy
Memory Aid
Picture a three-legged chair with one leg missing (m + r < 2j). You sit on it and it COLLAPSES — it's a mechanism, not a structure. Every time m + r is less than 2j, your truss is that unstable chair. Always count the legs before you sit!
Anchor Type
visual_association
Why It Works
The collapsing chair creates a fear-salience memory (you would not want to sit on it), which triggers stronger encoding than neutral images.
Example Usage
Truss with m=6, r=3, j=5: m+r=9, 2j=10. 9 < 10 → unstable. The chair is missing a leg — do not trust this structure!
Recall Trigger
Missing chair leg = m + r < 2j = unstable mechanism.
Tags
- process
- procedure
- common pitfall
Topic
Method of Joints
Concept
Support reactions must be found BEFORE solving any joint or section
Anchor Id
A15
Difficulty
easy
Memory Aid
A surveyor named Engineer Santos always starts any site work with BENCHMARKS (known reference points) before measuring anything else. In truss analysis, the reactions are your benchmarks. Without them, every joint you analyze is built on guesswork — your answers drift like measurements without a reference point. Engineer Santos never starts measuring without benchmarks, and you never start truss analysis without reactions.
Anchor Type
micro_story
Why It Works
The surveyor-benchmark analogy creates a professional identity hook. CE reviewees identify with the role of Engineer Santos, making the procedural rule personally meaningful.
Example Usage
Any truss problem: before writing a single equilibrium equation at a joint, solve for R_A and R_B from the whole-truss free body diagram. Reactions are your benchmarks.
Recall Trigger
Engineer Santos and his benchmarks = reactions first, always.
Tags
- conceptual
- strategy
- comparison
Topic
Method of Sections
Concept
When to use Method of Joints vs. Method of Sections
Anchor Id
A16
Difficulty
medium
Memory Aid
Method of Joints is like eating RICE one grain at a time — thorough but slow. You analyze EVERY member systematically from one end to the other. Method of Sections is like using a KNIFE to cut directly to the food you want — fast and targeted for just a few interior members. Use the rice method (Joints) when you need all forces. Use the knife method (Sections) when you need only 1-3 specific members deep inside the truss.
Anchor Type
analogy
Why It Works
Food-based analogies are highly effective in Filipino culture. The contrast between slow/thorough (rice grains) and fast/targeted (knife) maps perfectly to the two methods' strategic advantages.
Example Usage
Exam asks only for force in middle diagonal of a 10-panel truss: use the knife (Method of Sections) — cutting through 3 members near that diagonal avoids solving 20+ joints.
Recall Trigger
Rice grain by grain = Method of Joints; Kitchen knife = Method of Sections.
Tags
- formula
- sign convention
- process
Topic
Method of Joints
Concept
A negative member force answer means compression (given tension was assumed)
Anchor Id
A17
Difficulty
easy
Memory Aid
THE SIGN RULE IN 3 CHUNKS: (1) ASSUME = Tension is positive, always. (2) COMPUTE = Solve normally, keep the sign. (3) INTERPRET = Negative answer → flip to compression, label 'C'. Three chunks: Assume-Compute-Interpret (ACI). Bonus: ACI also stands for American Concrete Institute — so whenever you remember ACI 318, also remember the ACI sign rule for trusses!
Anchor Type
chunking
Why It Works
Chunking into 3 steps reduces cognitive load. The ACI double-meaning creates a cross-topic memory bridge (ACI 318 is also in the CE board syllabus), reinforcing both memories simultaneously.
Example Usage
F_AC = −15.63 kN. Assumed tension (A). Computed −15.63 (C). Interpreted: negative = compression, label as 15.63 kN (C). Done.
Recall Trigger
ACI: Assume tension, Compute, Interpret the sign.
Tags
- definition
- determinacy
- indeterminate
Topic
Determinacy
Concept
Truss determinacy: m + r > 2j means statically indeterminate
Anchor Id
A18
Difficulty
medium
Memory Aid
Picture a SIX-LEGGED table (m + r > 2j). It stands perfectly — in fact, it has TOO MANY legs. You cannot determine the force in each leg from statics alone because any combination of the extra legs could be carrying the load. This is exactly indeterminate: too many unknowns, statics is insufficient. You need advanced methods (compatibility, virtual work) to solve it.
Anchor Type
visual_association
Why It Works
The over-constrained table creates a spatial redundancy image. Over-supported = indeterminate is a direct structural analogy.
Example Usage
Truss: m=11, r=3, j=6. m+r=14, 2j=12. 14>12 → indeterminate to the second degree. Too many table legs — cannot solve by statics alone.
Recall Trigger
Six-legged table = too many supports = indeterminate.
Tags
- process
- geometry
- common pitfall
Topic
Method of Joints
Concept
Member angle calculation — must recompute geometry for each panel
Anchor Id
A19
Difficulty
medium
Memory Aid
During a board exam simulation, Engineer Reyes reused the angle from a previous panel without checking the new panel's geometry. Her diagonal was shorter but she used the longer panel's angle. Result: wrong forces, failing marks. Now she remembers: 'ALWAYS sketch the geometry and use arctan(height/horizontal run) for EACH member separately.' She calls this her 'expensive lesson in triangles.'
Anchor Type
micro_story
Why It Works
Learning from a cautionary story about exam failure creates a strong negative-consequence memory trace, which is one of the most effective forms of procedural memory encoding.
Example Usage
Before applying equilibrium at any joint: draw the member, write out its Δy and Δx, compute θ = arctan(Δy/Δx), find sinθ and cosθ. Never borrow an angle from a different panel.
Recall Trigger
Engineer Reyes's expensive lesson: recompute each member's angle individually.
Tags
- definition
- visual
- real-world application
Topic
Truss Definition
Concept
Truss is a rigid framework of straight members joined at ends
Anchor Id
A20
Difficulty
easy
Memory Aid
Think of the SKYWAY or METRO RAIL TRANSIT steel trusses you see on EDSA. Those steel triangles forming the bridge girder are exactly a truss — rigid, straight members, pin-connected at the joints, loads from the deck applied only at panel points. Every time you ride the MRT, you are inside a giant solved truss problem. The triangles cannot change shape under load — that is what makes a truss rigid.
Anchor Type
visual_association
Why It Works
Connecting the concept to a landmark Filipino infrastructure creates place-based memory (method of loci). The MRT is a daily-life object for Metro Manila reviewees, making the truss concept permanently grounded.
Example Usage
Introduction to any truss problem: mentally picture the MRT truss. Confirm the structure is made of straight members forming triangles with loads at joints only.
Recall Trigger
MRT trusses on EDSA = rigid triangular framework = truss definition.
Revision Game
m + r = 2j (the determinacy formula)
Clue
I am the magic formula that tells you if a truss can be solved by statics alone. Three letters, one number. What am I?
Memory Link
Anchor A1 — Mr. 2J the strict examiner
Two-force member (carries only axial tension or compression)
Clue
I am the kind of structural member that carries only a push or a pull — never a twist or a bend. A taho stick knows me well. What type of member am I?
Memory Link
Anchor A2 — The taho stick analogy
Zero-force member (under current loading, but still necessary)
Clue
I am the hardworking barangay tanod who appears to do nothing all day but cannot be removed from the truss. Remove me and the structure may buckle or fail under a different load. What am I called?
Memory Link
Anchor A11 — Barangay tanod micro-story
The vertical member is zero-force. Rule 2: two collinear + one odd member + no load → odd member is zero-force.
Clue
A truss joint has three members: two run horizontally along the chord, one vertical hangs down. No load acts at this joint. Which member is zero-force — and which rule applies?
Memory Link
Anchor A8 — Odd employee standing sideways
Method of Sections — cuts directly to the target member through ≤3 members, rather than solving all joints sequentially.
Clue
You need the force in ONE interior diagonal of a 20-panel truss. You have 10 minutes left in the board exam. Which analysis method is faster, and why is it like a kitchen knife?
Memory Link
Anchor A6 and A16 — Lumpia cut and kitchen knife analogy
Support reactions (from whole-truss free body diagram equilibrium)
Clue
I am the FIRST thing you must compute before solving ANY joint or section. Engineer Santos calls me his benchmarks. Without me, your entire truss solution floats in space. What am I?
Memory Link
Anchor A15 — Engineer Santos and his benchmarks
m+r = 18, 2j = 18. Equal → statically determinate (if also geometrically stable). Degree of indeterminacy = 0.
Clue
A truss has m=15, r=3, j=9. Compute m+r and 2j. Is this truss determinate, indeterminate, or unstable? To what degree?
Memory Link
Anchor A1 (Mr. 2J) and A10 (PRC papers analogy — still must check geometry)
Squinting face = compression. The top chord is in compression under downward gravity loads.
Clue
The top chord of a simply supported truss under gravity loading makes a face. Which face — a squint or a smile — and what force does it carry?
Memory Link
Anchor A12 — Squinting face (top chord compression) vs. smiling face (bottom chord tension)
Formula Mnemonics
Formula
m + r = 2j (Determinacy Check)
Mnemonic
MR. 2J — Members + Reactions must satisfy MR. 2J (Mr. Two-Joints). Strictly determinate when exactly equal. Less than 2j = mechanism; greater than 2j = indeterminate.
When To Use
Use this as the FIRST step before attempting any truss analysis. Verify the truss is statically determinate AND geometrically stable (arrangement must also be proper). Required in virtually every board-exam truss problem.
What Each Part Means
m = number of members (bars/sticks of the truss); r = number of external reaction components (e.g., pin = 2, roller = 1); j = number of joints (pin connections including supports); 2j = two equilibrium equations per joint (ΣFx=0 and ΣFy=0).
Formula
ΣFx = 0 and ΣFy = 0 at each joint (Method of Joints)
Mnemonic
XY BALANCE — every joint must balance in both the X and Y directions simultaneously. Picture a perfectly balanced taho cup on a flat tray: no tipping sideways (ΣFx=0), no tipping forward/backward (ΣFy=0).
When To Use
At every joint during Method of Joints analysis. Yields 2 equations per joint, matching 2 unknowns maximum per joint.
What Each Part Means
ΣFx = sum of all horizontal force components at the joint = 0 (horizontal equilibrium); ΣFy = sum of all vertical force components at the joint = 0 (vertical equilibrium). Member forces are projected using their angles: F·cosθ for x-component, F·sinθ for y-component.
Formula
ΣM_point = 0 about intersection of two cut members (Method of Sections)
Mnemonic
THE VANISHING ACT — take moments about the point where two unknowns VANISH (their lines of action pass through the moment point, so their moment arms are zero). Only the desired member remains — one equation, one unknown. 'Two disappear, one appears.'
When To Use
In Method of Sections when you need a specific interior member force efficiently. Cut the truss through ≤3 members, identify the intersection point of the two you do NOT want to solve for, and take moments there.
What Each Part Means
ΣM = sum of moments about a carefully chosen point = 0. The chosen point is the intersection of the lines of action of any two of the three cut members. This eliminates those two unknowns from the moment equation, leaving only the desired member force.
Formula
θ = arctan(Δy / Δx) for member angle computation
Mnemonic
RISE OVER RUN TO GET THE ANGLE — θ = arctan(rise/run) = arctan(vertical rise / horizontal run). Then: sinθ = rise/L, cosθ = run/L, where L = √(Δx² + Δy²). Draw a right triangle for EVERY member before projecting forces.
When To Use
Every time you resolve a diagonal member force into horizontal and vertical components. Critical step in both Method of Joints and Method of Sections — never skip this geometry step.
What Each Part Means
θ = inclination angle of the member from horizontal; Δy = difference in y-coordinates of the two end joints; Δx = difference in x-coordinates; L = member length = hypotenuse of the right triangle formed by Δx and Δy.
Formula
F_member (resolved) = F·sinθ (vertical) and F·cosθ (horizontal)
Mnemonic
SOH-CAH-TOA LIVES IN TRUSSES — Sin = Opposite/Hypotenuse gives the vertical projection (sinθ × F); Cos = Adjacent/Hypotenuse gives the horizontal projection (cosθ × F). The hypotenuse is always the member force F itself. Never mix these up: vertical component uses sine, horizontal uses cosine (for θ measured from horizontal).
When To Use
Every joint equation where a diagonal member is involved. Also used in Method of Sections when writing force equations (ΣFy=0 or ΣFx=0) for the cut free body.
What Each Part Means
F = magnitude of the member force (the unknown or known value along the member); sinθ = ratio of vertical leg to member length; cosθ = ratio of horizontal leg to member length; these components are substituted into ΣFy and ΣFx respectively.
Quick Recall Chains
Chain Title
Method of Joints — 5 Steps in Order (RAISE)
Recall Test
Without looking, list all 5 steps of Method of Joints using RAISE. What does each letter stand for? What happens if you skip R?
Memory Chain
RAISE your hand: R = Reactions first, A = Assume tension, I = Identify starting joint, S = Solve equilibrium, E = Extend to next joint. Engineer Santos RAISES his hand before every truss solution — it signals: 'I will not forget my benchmarks (reactions) and I will go step by step.'
Items To Remember
- Find support Reactions (whole-truss FBD)
- Assume all members in Tension (positive)
- Identify starting joint (only 2 unknowns)
- Solve ΣFx=0 and ΣFy=0 at each joint
- Extend to adjacent joints (carry known forces forward)
Chain Title
Checking Truss Type with m + r vs. 2j
Recall Test
A truss has 13 members, 3 reaction components, and 8 joints. What is m+r? What is 2j? What is the determinacy classification?
Memory Chain
PENCIL CHECK: P=Pin counts, E=External reactions totaled, N=Number of joints, C=Compute 2j, I=Inspect m+r vs 2j, L=Label the result (Det/Indet/Unstable). After the check, Mr. 2J either stamps APPROVED (=), REJECTED-COLLAPSE (<), or REJECTED-REDUNDANT (>).
Items To Remember
- Compute m (count all members)
- Compute r (count reaction components: pin=2, roller=1)
- Compute j (count all joints)
- Calculate m + r and compare to 2j
- m + r = 2j → determinate (and check geometry)
- m + r < 2j → unstable (mechanism)
- m + r > 2j → indeterminate (degree = m+r−2j)
Chain Title
Zero-Force Member Identification Rules
Recall Test
At joint K: three members connect — two run horizontally left and right (collinear along bottom chord), one runs vertically up. No load at K. Which member(s) are zero-force? Why?
Memory Chain
SCAN the truss like a security guard: S=Spot joints with 2 or 3 members, C=Check for external load at the joint, A=Apply Rule 1 (both zero) or Rule 2 (odd one out), N=Note and cross out zero-force members. The security guard (barangay tanod) may have zero tasks tonight but never gets fired.
Items To Remember
- Scan all joints for special configurations
- Rule 1: Joint with 2 non-collinear members + no load → BOTH are zero-force
- Rule 2: Joint with 3 members (2 collinear) + no load → ODD member is zero-force
- Mark and remove zero-force members to simplify
- Remember: zero-force ≠ useless (they still serve structural purposes)
Chain Title
Method of Sections — Targeted Attack Procedure
Recall Test
You need the force in diagonal member GH. You cut through GH, vertical GJ, and top chord FG. Where do you take moments? Why?
Memory Chain
TARGET-CUT-ISOLATE-INTERSECT-MOMENT-SOLVE (TCIIMS). A sniper (Method of Sections) does: T=Target acquired, C=Cut path planned (3 members max), I=Isolate the simpler side, I=Identify the intersection of the other two, M=Moment equation taken there, S=Solve. One shot, one kill — efficient and precise like a sniper.
Items To Remember
- Identify the target member (the one you need to find)
- Draw a cut through the target and at most 2 other members (total ≤ 3)
- Isolate one side as a free body
- Locate the intersection point of the two non-target cut members
- Take ΣM = 0 about that intersection point
- Solve the single remaining unknown
Chain Title
Truss Assumptions and Why Each Matters
Recall Test
State the three truss assumptions. For each, explain what structural simplification it enables. What is a two-force member and which assumption produces it?
Memory Chain
FLS = Feel Less Stress: Frictionless (no moment at joints), Loads-at-joints (no midspan bending), Straight (pure axial force direction). All three together make EVERY member a two-force member. If FLS fails, you are no longer analyzing a truss — you are analyzing a frame, and life gets much harder.
Items To Remember
- Frictionless pin connections → no moment transfer at joints → members are pure axial
- Loads at joints only → no bending in members → two-force member behavior
- Straight members → force direction is along the member axis
- All three together → every member carries only tension or compression
- Violation of any assumption → member analysis becomes beam-column, not truss
Ready to practise for the CELE 2026?
Super Tutor's AI review plan adapts to your weak areas and builds a weekly practice schedule around your target CELE exam date.