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CELE Steel & Timber DesignSteel Tension MembersExam Answer Templates

Exam answer templates for Steel Tension Members in CELE Steel & Timber Design. These are the response frameworks that consistently earn full marks on Professional Regulation Commission (PRC) — Board of Civil Engineering's questions. Each template is tuned to a specific question type — learn them all and your CELE 2026 performance will reflect it.

Exam context

Professional Regulation Commission (PRC) — Board of Civil Engineering runs the Civil Engineer Licensure Examination on May and November 2026. Its Steel & Timber Design section sits under a "Core" weighting, and Steel Tension Members is the 1st chapter in the 5-chapter CELE Steel & Timber Design rotation. The CELE passing mark is 70% weighted average, no sub-test below 50%, and the most recent 2026 paper drew about a meaningful share of questions from Steel & Timber Design.

Steel Tension Members - Exam Answer Templates

Proper answer writing is the bridge between knowing the material and earning full marks on the PRC Civil Engineer Licensure Examination. In Steel & Timber Design, examiners award marks for three things: correct formula identification, accurate substitution with correct units, and a clear conclusion statement. A student who knows the concept but writes a disorganized answer loses marks to a well-structured competitor. These templates show you exactly how a full-mark answer looks — word for word, line by line — so you can replicate that structure under exam pressure. Study the scoring breakdown, memorize the key phrases, and practice writing answers within the allotted time.

Templates

State the two limit states for the design of a steel tension member under NSCP 2015.

Marks

1

Topic

Two Limit States

Difficulty

easy

Template Id

T1

Examiner Tip

This is a 1-mark definition question; examiners want a complete, paired answer. A one-word response like 'yielding and rupture' earns zero — you must include the φ factors and area terms.

Model Answer

The two limit states are: (1) Tensile yielding on the gross area: φPn = 0.90 Fy Ag, and (2) Tensile rupture on the effective net area: φPn = 0.75 Fu Ae. The lower value governs.

Question Type

very_short_answer

Answer Structure

  • Line 1: Name both limit states with their resistance factors and area references [1 mark]

Scoring Breakdown

Marks

1

Criteria

Both limit states named with correct φ values (0.90 for yielding, 0.75 for rupture) and correct area terms (Ag for yielding, Ae for rupture)

Common Mark Deductions

  • Stating only one limit state (-1 mark, i.e., zero)
  • Swapping the φ factors (0.75 for yield, 0.90 for rupture) — a fatal error
  • Using 'net area An' instead of 'effective net area Ae' for the rupture limit state

Key Phrases To Include

  • tensile yielding
  • gross area Ag
  • φ = 0.90
  • tensile rupture
  • effective net area Ae
  • φ = 0.75
  • lower value governs

Define the shear-lag factor U and state when U = 1.0 is applicable for a tension member.

Marks

2

Topic

Shear-Lag Factor

Difficulty

easy

Template Id

T2

Examiner Tip

Give a concrete example (plate bolted full-width vs. angle bolted one leg) — examiners reward practical application of the concept.

Model Answer

The shear-lag factor U accounts for the non-uniform stress distribution across a cross-section when not all elements are directly connected at a joint. It reduces the net area to give the effective net area: Ae = U·An, where U ≤ 1.0. U = 1.0 is applicable when the tensile load is transmitted through ALL cross-sectional elements (e.g., a plate bolted across its entire width, or a W-section with both flanges and web connected). When only one leg of an angle or one flange of a tee is connected, U < 1.0.

Question Type

short_answer

Answer Structure

  • Line 1–2: Define U and write the formula Ae = U·An [1 mark]
  • Line 3–4: State the condition for U = 1.0 and give one example where U < 1.0 [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct definition of shear lag (non-uniform stress when not all elements connected) and formula Ae = U·An

Marks

1

Criteria

Correct condition for U = 1.0 (all elements connected) AND acknowledgment that U < 1.0 for partial connections (e.g., angle bolted through one leg)

Common Mark Deductions

  • Defining U without the formula Ae = U·An
  • Stating U = 1.0 'always' without specifying the connection condition
  • Confusing An (net area) with Ae (effective net area)

Key Phrases To Include

  • shear lag
  • non-uniform stress
  • Ae = U·An
  • U ≤ 1.0
  • all cross-sectional elements connected
  • U = 1.0

Explain why two different resistance factors (φ = 0.90 and φ = 0.75) are used for the two tensile limit states.

Marks

2

Topic

Resistance Factors

Difficulty

medium

Template Id

T3

Examiner Tip

Use the words 'ductile' and 'brittle' explicitly — these are the engineering-precise terms examiners want to see.

Model Answer

The difference in φ reflects the relative predictability and consequence of each failure mode: φ = 0.90 for yielding: Yielding is ductile and gradual — there is visible deformation and warning before failure. The gross-area and material yield strength Fy are well-defined, so a higher φ (less conservatism) is justified. φ = 0.75 for rupture: Fracture at the net section is sudden and brittle — there is little or no warning. Additionally, Fu (ultimate strength) has greater variability than Fy, and hole quality introduces uncertainty. A lower φ (more conservatism) is therefore required.

Question Type

short_answer

Answer Structure

  • Line 1–2: Explain why φ = 0.90 is used for yielding (ductile, predictable, Fy well-defined) [1 mark]
  • Line 3–4: Explain why φ = 0.75 is used for rupture (brittle, sudden, Fu more variable, hole uncertainty) [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct reasoning for φ = 0.90: ductile/gradual failure mode AND well-defined Fy

Marks

1

Criteria

Correct reasoning for φ = 0.75: brittle/sudden fracture AND greater uncertainty in Fu or hole quality

Common Mark Deductions

  • Simply stating 'rupture is more dangerous' without linking to ductility or variability
  • Reversing the explanation (calling yielding brittle or rupture ductile)
  • Not mentioning the consequence of hole-related uncertainty

Key Phrases To Include

  • ductile
  • gradual
  • visible deformation
  • Fy well-defined
  • brittle
  • sudden
  • no warning
  • Fu variability
  • conservatism

What hole diameter should be used for net-area calculation when 20 mm diameter bolts are used in a punched hole? Briefly justify.

Marks

1

Topic

Net Area Calculation

Difficulty

easy

Template Id

T4

Examiner Tip

Write the formula dh = db + 2 mm explicitly before substituting — this shows the examiner you know the rule, not just the number.

Model Answer

Use dh = 20 + 2 = 22 mm. The 2 mm allowance accounts for the punching/drilling damage to the surrounding material beyond the nominal hole diameter. (Some references use +3 mm total, giving dh = 23 mm; either value is acceptable if the basis is stated.)

Question Type

very_short_answer

Answer Structure

  • Line 1: State dh = db + 2 mm = 22 mm with brief justification [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct hole diameter (22 mm or 23 mm depending on assumed allowance) AND reason for the addition (punching damage / clearance)

Common Mark Deductions

  • Using the bolt diameter (20 mm) directly without adding the clearance — most common error
  • Adding 3 mm but not stating the basis
  • Using 25 mm (standard bolt clearance hole) which applies to hole fabrication, not the design deduction

Key Phrases To Include

  • dh = db + 2 mm
  • 22 mm
  • punching damage
  • clearance allowance
  • net area

A 250 mm × 12 mm steel plate (Fy = 248 MPa, Fu = 400 MPa) is connected with two 22 mm diameter bolts in a single row perpendicular to the load (dh = 24 mm, U = 1.0). Determine the design tensile strength φPn.

Marks

5

Topic

Two Limit States — Full Design Check

Difficulty

medium

Template Id

T5

Examiner Tip

Write 'Limit State 1' and 'Limit State 2' explicitly as headings — it signals to the examiner that you are systematically checking both, which is the NSCP 2015 requirement.

Model Answer

GIVEN: Plate: 250 mm × 12 mm Fy = 248 MPa, Fu = 400 MPa Bolt diameter = 22 mm → dh = 24 mm Number of bolts in critical section = 2 U = 1.0 STEP 1 — Gross Area: Ag = 250 × 12 = 3 000 mm² STEP 2 — Net Area: An = Ag − n(dh × t) = 3 000 − 2(24)(12) An = 3 000 − 576 = 2 424 mm² STEP 3 — Effective Net Area: Ae = U·An = 1.0 × 2 424 = 2 424 mm² STEP 4 — Limit State 1: Tensile Yielding (φ = 0.90) φPn,yield = 0.90 × Fy × Ag = 0.90 × 248 × 3 000 φPn,yield = 669 600 N = 669.6 kN STEP 5 — Limit State 2: Tensile Rupture (φ = 0.75) φPn,rupture = 0.75 × Fu × Ae = 0.75 × 400 × 2 424 φPn,rupture = 727 200 N = 727.2 kN STEP 6 — Governing Design Strength: φPn = min(669.6, 727.2) = 669.6 kN CONCLUSION: The design tensile strength is φPn = 669.6 kN. Yielding on the gross section governs.

Question Type

numerical

Answer Structure

  • Section 1: List all given data clearly [0.5 mark implicit — shows organized thinking]
  • Step 1: Compute Ag correctly [0.5 mark]
  • Step 2: Compute An with correct dh and subtraction [1 mark]
  • Step 3: Compute Ae = U·An [0.5 mark]
  • Step 4: Compute φPn,yield = 0.90 Fy Ag [1 mark]
  • Step 5: Compute φPn,rupture = 0.75 Fu Ae [1 mark]
  • Step 6: Select the lower value and state which limit state governs [0.5 mark]

Scoring Breakdown

Marks

1

Criteria

Correct Ag = 3 000 mm² and correct An = 2 424 mm² (using dh = 24 mm, not 22 mm)

Marks

1

Criteria

Correct Ae = 2 424 mm² (U = 1.0 applied)

Marks

1

Criteria

Correct yielding calculation: φPn = 0.90 × 248 × 3 000 = 669.6 kN

Marks

1

Criteria

Correct rupture calculation: φPn = 0.75 × 400 × 2 424 = 727.2 kN

Marks

1

Criteria

Correct conclusion: minimum selected (669.6 kN) with statement that yielding governs

Common Mark Deductions

  • Using bolt diameter (22 mm) instead of hole diameter (24 mm) for net-area subtraction — loses the An and all subsequent marks
  • Skipping either the yielding or rupture limit state
  • Using φ = 0.75 for yielding or φ = 0.90 for rupture
  • Omitting the conclusion statement about which limit state governs
  • Missing units (N vs. kN) causing incorrect final answer

Key Phrases To Include

  • Ag = 250 × 12
  • dh = 24 mm
  • An = Ag − n(dh)(t)
  • Ae = U·An
  • φPn,yield = 0.90 Fy Ag
  • φPn,rupture = 0.75 Fu Ae
  • yielding governs
  • minimum

A 200 mm-wide, 10 mm-thick plate has three 20 mm bolts (dh = 22 mm) arranged in two staggered lines. The stagger pitch is s = 60 mm and the transverse gage is g = 80 mm. The potential failure path crosses two holes with one stagger segment. Compute the net width and net area.

Marks

3

Topic

Staggered Holes — Net Area

Difficulty

medium

Template Id

T6

Examiner Tip

Always compare ALL failure paths (straight and zigzag) and state which gives the smallest net area — this comparison earns an often-overlooked mark.

Model Answer

GIVEN: Plate width Wg = 200 mm, thickness t = 10 mm dh = 22 mm, s = 60 mm, g = 80 mm Failure path: 2 holes + 1 stagger segment STEP 1 — Net Width Formula (NSCP 2015 / AISC 360-D3): wnet = Wg − Σdh + Σ(s²/4g) STEP 2 — Substitute: wnet = 200 − 2(22) + (60²)/(4 × 80) wnet = 200 − 44 + 3 600/320 wnet = 200 − 44 + 11.25 wnet = 167.25 mm STEP 3 — Net Area: An = wnet × t = 167.25 × 10 = 1 672.5 mm² CONCLUSION: The net width is 167.25 mm and the net area for this failure path is An = 1 672.5 mm². (Note: The straight path across 1 hole gives An = (200 − 22) × 10 = 1 780 mm². The staggered path (1 672.5 mm²) is smaller and therefore governs.)

Question Type

numerical

Answer Structure

  • Step 1: Write the staggered net-width formula [1 mark]
  • Step 2: Substitute values correctly (dh, s, g) and compute wnet [1 mark]
  • Step 3: Compute An = wnet × t and state which path governs [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct formula: wnet = Wg − Σdh + Σ(s²/4g)

Marks

1

Criteria

Correct numerical substitution leading to wnet = 167.25 mm

Marks

1

Criteria

Correct An = 1 672.5 mm² AND comparison with straight-path An to identify governing path

Common Mark Deductions

  • Forgetting the s²/4g term entirely — most common error in staggered-hole problems
  • Using bolt diameter (20 mm) instead of hole diameter (22 mm)
  • Not checking the straight-path net area for comparison
  • Computing s²/4g incorrectly (e.g., dividing by 4g² instead of 4g)

Key Phrases To Include

  • wnet = Wg − Σdh + Σ(s²/4g)
  • stagger
  • s = 60 mm
  • g = 80 mm
  • s²/4g = 11.25 mm
  • governing net area

State the recommended slenderness limit for steel tension members per NSCP 2015 and explain whether it is mandatory.

Marks

1

Topic

Slenderness Recommendation

Difficulty

easy

Template Id

T7

Examiner Tip

The word 'recommended' is a key differentiator from compression member limits. Use it explicitly.

Model Answer

Per NSCP 2015 (AISC 360 Section D1), the recommended slenderness limit for tension members is L/r ≤ 300. This limit is a recommendation, not a mandatory requirement (except for rods, which are exempt). It is provided to prevent excessive sag and vibration under service conditions.

Question Type

very_short_answer

Answer Structure

  • Line 1: State L/r ≤ 300 with code reference [0.5 mark]
  • Line 2: Clarify that it is recommended, not mandatory [0.5 mark]

Scoring Breakdown

Marks

1

Criteria

Correct limit (L/r ≤ 300) AND correct characterization as a recommendation (not mandatory)

Common Mark Deductions

  • Stating L/r ≤ 300 is mandatory (it is only recommended)
  • Citing the compression member limit (L/r ≤ 200) instead
  • Omitting the reason (sag/vibration) when the question asks for an explanation

Key Phrases To Include

  • L/r ≤ 300
  • recommended
  • not mandatory
  • sag
  • vibration

An L75×75×8 angle (Ag = 1 150 mm², Fy = 248 MPa, Fu = 400 MPa) is connected through one leg with a single 20 mm bolt (dh = 22 mm). Given U = 0.85, determine the design tensile strength φPn.

Marks

5

Topic

Angle Tension Member with Shear Lag

Difficulty

hard

Template Id

T8

Examiner Tip

In angle problems, rupture often governs because U < 1.0 substantially reduces Ae. Warn yourself at the start: 'angle + one leg = shear lag = U < 1.0.'

Model Answer

GIVEN: Angle: L75×75×8, Ag = 1 150 mm² Fy = 248 MPa, Fu = 400 MPa Bolt: 20 mm diameter → dh = 22 mm Connected leg thickness = 8 mm U = 0.85 (shear lag, one leg connected) STEP 1 — Gross Area: Ag = 1 150 mm² (given) STEP 2 — Net Area: An = Ag − dh × t = 1 150 − 22 × 8 An = 1 150 − 176 = 974 mm² STEP 3 — Effective Net Area: Ae = U × An = 0.85 × 974 = 827.9 mm² STEP 4 — Limit State 1: Tensile Yielding (φ = 0.90) φPn,yield = 0.90 × 248 × 1 150 φPn,yield = 256 680 N = 256.7 kN STEP 5 — Limit State 2: Tensile Rupture (φ = 0.75) φPn,rupture = 0.75 × 400 × 827.9 φPn,rupture = 248 370 N = 248.4 kN STEP 6 — Governing Design Strength: φPn = min(256.7, 248.4) = 248.4 kN CONCLUSION: The design tensile strength is φPn = 248.4 kN. Tensile rupture on the effective net section governs.

Question Type

numerical

Answer Structure

  • Step 1: Identify Ag (given) [implicit]
  • Step 2: Compute An = Ag − dh × t (one hole, one leg) [1 mark]
  • Step 3: Compute Ae = U × An with U = 0.85 [1 mark]
  • Step 4: Compute φPn,yield = 0.90 × 248 × 1 150 [1 mark]
  • Step 5: Compute φPn,rupture = 0.75 × 400 × 827.9 [1 mark]
  • Step 6: Select minimum and state governing limit state [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct An = 974 mm² (one hole, 22 mm × 8 mm deduction)

Marks

1

Criteria

Correct Ae = 827.9 mm² (U = 0.85 applied to An)

Marks

1

Criteria

Correct φPn,yield = 256.7 kN

Marks

1

Criteria

Correct φPn,rupture = 248.4 kN

Marks

1

Criteria

Correct minimum selection (248.4 kN) with statement that rupture governs

Common Mark Deductions

  • Using U = 1.0 (ignoring shear lag for an angle bolted through one leg)
  • Applying U to Ag instead of An
  • Using the wrong leg thickness (using 75 mm instead of 8 mm for hole deduction)
  • Not comparing both limit states

Key Phrases To Include

  • An = Ag − dh × t
  • Ae = U × An = 0.85 × 974
  • shear lag
  • one leg connected
  • φPn,yield = 0.90 Fy Ag
  • φPn,rupture = 0.75 Fu Ae
  • rupture governs

A tension member is 5.0 m long and has a least radius of gyration r = 15 mm. Check whether the slenderness recommendation of NSCP 2015 is satisfied.

Marks

2

Topic

Slenderness Check

Difficulty

easy

Template Id

T9

Examiner Tip

Always show the unit conversion (5.0 m → 5 000 mm) explicitly — examiners give credit for dimensional consistency.

Model Answer

GIVEN: Length L = 5.0 m = 5 000 mm Least radius of gyration r = 15 mm STEP 1 — Compute Slenderness Ratio: L/r = 5 000 / 15 = 333.3 STEP 2 — Compare with Recommendation: NSCP 2015 (AISC 360 D1) recommends L/r ≤ 300 for tension members. 333.3 > 300 → NOT SATISFIED. CONCLUSION: The slenderness ratio L/r = 333.3 exceeds the recommended limit of 300. Although this is not a mandatory failure, the member may experience unacceptable sag or vibration and the designer should select a section with larger r.

Question Type

numerical

Answer Structure

  • Step 1: Compute L/r = 5 000 / 15 = 333.3 [1 mark]
  • Step 2: Compare with limit 300 and state pass/fail + recommendation [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct L/r = 333.3 (with L converted to mm)

Marks

1

Criteria

Correct conclusion (333.3 > 300, not satisfied) AND note that the limit is a recommendation (not mandatory)

Common Mark Deductions

  • Forgetting to convert L to mm (using L = 5.0 directly gives L/r = 0.33 — nonsensical)
  • Stating the member 'fails' without clarifying that the limit is only a recommendation
  • Not providing a conclusion or remediation comment

Key Phrases To Include

  • L/r = 333.3
  • recommended limit 300
  • not satisfied
  • recommendation not mandatory
  • sag or vibration

Derive the net width formula for staggered bolt holes: wnet = Wg − Σdh + Σ(s²/4g). Identify what each symbol represents.

Marks

3

Topic

Staggered Holes — Formula Derivation

Difficulty

medium

Template Id

T10

Examiner Tip

If you sketch the bolt pattern showing the diagonal failure path, you earn the explanation mark visually — a 30-second sketch saves 3 lines of written explanation.

Model Answer

The staggered net-width formula accounts for a diagonal failure path through staggered holes: wnet = Wg − Σdh + Σ(s²/4g) Where: wnet = net width of the failure path (mm) Wg = gross width of the plate (mm) Σdh = sum of all hole diameters on the failure path (mm); each dh = bolt diameter + 2 mm allowance s = longitudinal center-to-center spacing (pitch) between adjacent holes on the diagonal path (mm) g = transverse center-to-center spacing (gage) between adjacent bolt lines (mm) s²/4g = empirical correction added for each diagonal segment to account for the longer path Physical Basis: A diagonal path through staggered holes is longer than a straight-line path. The term s²/4g (derived from the Cochrane formula) partially compensates for this longer path by adding back some effective width. However, the net deduction is still larger than for a straight path through fewer holes when multiple staggered holes exist. Note: All possible failure paths (straight and zigzag) must be evaluated; the path giving the smallest wnet (hence smallest An) governs.

Question Type

short_answer

Answer Structure

  • Line 1–2: Write the formula with correct symbols [1 mark]
  • Lines 3–8: Define each symbol (Wg, dh, s, g, s²/4g) with physical meaning [1 mark]
  • Lines 9–12: Explain the physical basis of the s²/4g term and the need to check all paths [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct complete formula with all terms (Wg, Σdh, Σs²/4g)

Marks

1

Criteria

Correct definition of all four variables (Wg, dh, s, g) with units and the meaning of s²/4g

Marks

1

Criteria

Physical explanation of why s²/4g is added (diagonal path compensation) and the requirement to check all failure paths

Common Mark Deductions

  • Subtracting s²/4g instead of adding it
  • Confusing pitch (s, longitudinal) with gage (g, transverse)
  • Omitting the note about checking all failure paths

Key Phrases To Include

  • wnet = Wg − Σdh + Σ(s²/4g)
  • pitch s
  • gage g
  • diagonal failure path
  • Cochrane formula
  • all failure paths must be checked
  • smallest net area governs

Size a round solid steel tie rod (Fy = 248 MPa, Fu = 400 MPa) for a factored tensile load Pu = 200 kN, considering only the yielding limit state.

Marks

3

Topic

Sizing a Tension Member

Difficulty

medium

Template Id

T11

Examiner Tip

Always round UP when sizing members — a 33.78 mm rod means you must use 35 mm (next commercial size), never 33 mm. Write 'round up' explicitly.

Model Answer

GIVEN: Pu = 200 kN = 200 000 N Fy = 248 MPa, Fu = 400 MPa Round solid rod → no bolt holes in the typical sizing (threaded ends may reduce area, but problem specifies yielding limit state) STEP 1 — Required Gross Area (Yielding): φPn ≥ Pu → 0.90 × Fy × Ag ≥ Pu Ag,req = Pu / (0.90 × Fy) Ag,req = 200 000 / (0.90 × 248) Ag,req = 200 000 / 223.2 = 896.1 mm² STEP 2 — Required Diameter: Ag = π d² / 4 → d = √(4 Ag / π) d = √(4 × 896.1 / π) d = √(1 140.9) = 33.78 mm STEP 3 — Select Standard Size: Use d = 35 mm (round up to next standard size) Check: Ag = π(35)²/4 = 962.1 mm² φPn = 0.90 × 248 × 962.1 = 214 740 N = 214.7 kN > 200 kN ✓ CONCLUSION: Use a 35 mm diameter solid round tie rod. φPn = 214.7 kN > Pu = 200 kN — yielding limit state satisfied.

Question Type

numerical

Answer Structure

  • Step 1: Apply φPn ≥ Pu for yielding to find Ag,req [1 mark]
  • Step 2: Convert Ag to required diameter using Ag = πd²/4 [1 mark]
  • Step 3: Round up to practical size and verify φPn > Pu [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct Ag,req = 896.1 mm² using Ag = Pu / (0.90 Fy)

Marks

1

Criteria

Correct d = 33.78 mm from Ag = πd²/4 with algebra shown

Marks

1

Criteria

Rounding up to d = 35 mm (not 33 mm) with verification check φPn > Pu

Common Mark Deductions

  • Forgetting to convert Pu from kN to N (200 vs. 200 000)
  • Rounding down the diameter (33 mm instead of 35 mm) — unsafe design
  • Omitting the final verification check

Key Phrases To Include

  • φPn ≥ Pu
  • Ag,req = Pu / (0.90 Fy)
  • Ag = πd²/4
  • round up
  • verify
  • yielding limit state

Differentiate between net area An and effective net area Ae. When are they equal?

Marks

2

Topic

Net Area vs. Effective Net Area

Difficulty

easy

Template Id

T12

Examiner Tip

Use a contrast structure ('An accounts for... whereas Ae accounts for...') — it signals clear understanding of the two-step area calculation.

Model Answer

Net Area (An): The gross cross-sectional area minus the material removed by bolt holes at the critical section. Formula: An = Ag − Σ(dh × t). It accounts only for the geometric reduction due to holes. Effective Net Area (Ae): The net area further reduced by the shear-lag factor U to reflect the non-uniform stress distribution when not all cross-sectional elements are connected at the joint. Formula: Ae = U × An, where U ≤ 1.0. An = Ae when U = 1.0, which occurs when the tensile force is transmitted through ALL elements of the cross-section (e.g., a plate fully bolted across its entire width, or a W-section with both flanges and web connected at the joint). In this case, shear lag is absent and no further reduction is needed.

Question Type

short_answer

Answer Structure

  • Lines 1–2: Define An with formula [0.5 mark]
  • Lines 3–4: Define Ae with formula [0.5 mark]
  • Lines 5–6: State and justify when An = Ae (U = 1.0, all elements connected) [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct definitions of both An (holes subtracted from Ag) and Ae (U applied to An) with formulas

Marks

1

Criteria

Correct condition for An = Ae: U = 1.0 when all cross-sectional elements are connected, with an example

Common Mark Deductions

  • Defining An and Ae identically (not distinguishing shear lag)
  • Stating An = Ae without justifying why (U = 1.0 condition not stated)
  • Omitting examples or conditions

Key Phrases To Include

  • An = Ag − Σ(dh × t)
  • Ae = U × An
  • shear lag
  • U = 1.0
  • all elements connected
  • non-uniform stress

A 150 mm × 10 mm plate (Fy = 250 MPa, Fu = 410 MPa) carries a factored tensile load Pu = 280 kN. It is connected with two 16 mm bolts (dh = 18 mm, U = 1.0). Check adequacy.

Marks

5

Topic

Full Adequacy Check — Tension Plate

Difficulty

medium

Template Id

T13

Examiner Tip

The adequacy check (Step 7) is often the easiest mark but is forgotten under time pressure. Always write 'φPn ___ Pu → ADEQUATE / INADEQUATE' as your last line.

Model Answer

GIVEN: Plate: 150 mm × 10 mm Fy = 250 MPa, Fu = 410 MPa Pu = 280 kN = 280 000 N Bolts: 2 × 16 mm → dh = 18 mm U = 1.0 STEP 1 — Gross Area: Ag = 150 × 10 = 1 500 mm² STEP 2 — Net Area: An = Ag − n(dh × t) = 1 500 − 2(18)(10) An = 1 500 − 360 = 1 140 mm² STEP 3 — Effective Net Area: Ae = U × An = 1.0 × 1 140 = 1 140 mm² STEP 4 — Yielding Capacity: φPn,yield = 0.90 × 250 × 1 500 = 337 500 N = 337.5 kN STEP 5 — Rupture Capacity: φPn,rupture = 0.75 × 410 × 1 140 = 350 550 N = 350.6 kN STEP 6 — Governing Capacity: φPn = min(337.5, 350.6) = 337.5 kN (yielding governs) STEP 7 — Adequacy Check: φPn = 337.5 kN > Pu = 280 kN ✓ ADEQUATE CONCLUSION: The 150×10 plate is adequate. Design strength φPn = 337.5 kN exceeds the factored load Pu = 280 kN. Yielding on the gross section governs.

Question Type

numerical

Answer Structure

  • Steps 1–3: Area computations (Ag, An, Ae) [1 mark]
  • Step 4: Yielding capacity [1 mark]
  • Step 5: Rupture capacity [1 mark]
  • Step 6: Governing value identified [1 mark]
  • Step 7: Adequacy check (φPn vs. Pu) with conclusion [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct Ag = 1 500 mm², An = 1 140 mm², Ae = 1 140 mm²

Marks

1

Criteria

Correct yielding capacity: 0.90 × 250 × 1 500 = 337.5 kN

Marks

1

Criteria

Correct rupture capacity: 0.75 × 410 × 1 140 = 350.6 kN

Marks

1

Criteria

Correct governing value (337.5 kN) with identification of yielding as controlling limit state

Marks

1

Criteria

Correct adequacy conclusion: 337.5 kN > 280 kN → ADEQUATE

Common Mark Deductions

  • Using 16 mm instead of 18 mm for hole diameter
  • Stopping after calculating one limit state
  • Not writing the adequacy conclusion statement
  • Errors in unit conversion (kN vs. N)

Key Phrases To Include

  • φPn ≥ Pu
  • ADEQUATE
  • yielding governs
  • minimum
  • dh = 18 mm (not 16 mm)

Explain the term 'block shear' in the context of steel tension members. Write the NSCP 2015 (AISC 360) formula for block shear rupture strength.

Marks

3

Topic

Block Shear

Difficulty

hard

Template Id

T14

Examiner Tip

Board exams frequently ask for the formula with all symbols defined. Write the formula first, then define symbols below — this ordered approach avoids omissions.

Model Answer

Block Shear: A failure mode at bolt connections where a block of material tears out, combining SHEAR yielding or rupture along one plane and TENSION rupture along a perpendicular plane. It is a third limit state (in addition to gross yielding and net section rupture) that must be checked at the connection region. NSCP 2015 / AISC 360 Section J4.3 — Block Shear Rupture Strength: Rn = 0.60 Fu Anv + Ubs Fu Ant ≤ 0.60 Fy Agv + Ubs Fu Ant Where: Agv = gross area subject to shear Anv = net area subject to shear Ant = net area subject to tension Ubs = 1.0 for uniform tension stress; 0.50 for non-uniform tension stress φ = 0.75 (LRFD), Ω = 2.00 (ASD) The two expressions represent: (1) shear rupture + tension rupture [first term], and (2) shear yielding + tension rupture [second term]. The LOWER of the two governs (upper-bound limit on the shear term).

Question Type

short_answer

Answer Structure

  • Lines 1–2: Define block shear (combined shear + tension failure at connection) [1 mark]
  • Lines 3–5: Write the complete NSCP 2015 formula with both terms [1 mark]
  • Lines 6–8: Define all symbols and identify which expression governs [1 mark]

Scoring Breakdown

Marks

1

Criteria

Correct conceptual definition: simultaneous shear + tension failure, tearout of a block at connection

Marks

1

Criteria

Correct formula with both expressions: Rn = 0.60Fu·Anv + Ubs·Fu·Ant ≤ 0.60Fy·Agv + Ubs·Fu·Ant

Marks

1

Criteria

Correct symbol definitions (Agv, Anv, Ant, Ubs) AND statement that the smaller value governs (the inequality is an upper-bound)

Common Mark Deductions

  • Confusing block shear with net-section rupture (they occur in different planes)
  • Writing only one of the two expressions (the inequality is part of the formula)
  • Omitting Ubs (and hence the distinction between uniform and non-uniform tension)

Key Phrases To Include

  • block shear
  • tearout
  • shear rupture
  • tension rupture
  • Rn = 0.60 Fu Anv + Ubs Fu Ant
  • Agv, Anv, Ant
  • Ubs = 1.0 or 0.50
  • φ = 0.75

List FOUR common board-exam pitfalls in solving steel tension member problems and briefly explain how to avoid each.

Marks

3

Topic

Common Pitfalls

Difficulty

easy

Template Id

T15

Examiner Tip

For 'list and explain' questions, always match each item with an explicit avoidance action — passive lists earn 50% of available marks; action-based answers earn full marks.

Model Answer

Four Common Pitfalls and How to Avoid Them: 1. Using bolt diameter (db) instead of hole diameter (dh) for net area: Avoid by always writing dh = db + 2 mm (or +3 mm) before computing An. 2. Skipping a limit state (checking only yield or only rupture): Avoid by using a two-column layout: compute both φPn,yield and φPn,rupture, then take the minimum. 3. Applying U = 1.0 to angles/tees bolted through one leg: Avoid by flagging: 'angle + one leg connected → shear lag → U < 1.0' at the start of the problem. 4. Using the wrong resistance factor (φ = 0.90 for rupture or φ = 0.75 for yield): Avoid by writing a memory rule: 'Yield = 0.90 (higher φ, lower F); Rupture = 0.75 (lower φ, higher F).'

Question Type

short_answer

Answer Structure

  • Pitfall 1: Hole diameter error + avoidance strategy [0.75 mark]
  • Pitfall 2: Missing limit state + avoidance strategy [0.75 mark]
  • Pitfall 3: Shear lag assumption + avoidance strategy [0.75 mark]
  • Pitfall 4: Wrong φ factor + memory aid [0.75 mark]

Scoring Breakdown

Marks

1

Criteria

Any two pitfalls correctly identified with actionable avoidance strategies

Marks

2

Criteria

All four pitfalls correctly identified with specific avoidance strategies for each

Marks

3

Criteria

All four pitfalls identified with precise strategies AND at least one memory aid or worked-example reference included

Common Mark Deductions

  • Listing pitfalls without avoidance strategies
  • Repeating the same pitfall in different words
  • Vague answers like 'be careful' without specific guidance

Key Phrases To Include

  • dh = db + 2 mm
  • both limit states
  • shear lag
  • U < 1.0
  • φ = 0.90 for yield
  • φ = 0.75 for rupture

Mark Wise Strategy

Dos

  • Write the answer in the first sentence — do not build up to it
  • Include the code reference if the question asks for a code provision
  • Use engineering notation (e.g., 'dh = db + 2 mm = 22 mm') even for simple facts

Donts

  • Do not write lengthy introductions for a 1-mark question
  • Do not leave out the unit even for a simple number
  • Do not qualify your answer with 'I think' or 'maybe'

Marks

1

Strategy

State the key fact, formula, or value directly. No preamble. Include units. Use keywords the examiner is scanning for (e.g., 'yielding,' 'φ = 0.90,' 'L/r ≤ 300').

Expected Length

1–2 lines or a single formula with result

Time Allocation

1–1.5 minutes

Dos

  • Write two clearly separated points or steps — one per mark
  • For definitions, always write the formula after the words
  • Contrast related concepts (An vs. Ae, yield vs. rupture) to show understanding

Donts

  • Do not write a 10-line essay for a 2-mark question
  • Do not give only a formula without words, or only words without a formula
  • Do not mix up step 1 and step 2 — label them explicitly

Marks

2

Strategy

Structure as: (1) state the concept/formula, then (2) apply or elaborate with one concrete example or numerical step. For calculations, show at least two numbered steps. For theory, use a contrast or comparison structure.

Expected Length

3–5 lines or a 2-step calculation

Time Allocation

2–3 minutes

Dos

  • Label each step (Step 1, Step 2, Step 3) for numerical solutions
  • Write 'Given:' data block at the top — it signals organized problem-solving
  • End with a one-line conclusion that echoes the question

Donts

  • Do not skip the Given block — it costs no time and shows context
  • Do not combine two marks into one muddled paragraph
  • Do not use vague conclusions like 'the answer is correct'

Marks

3

Strategy

For numerical: Given → Formula → Substitution → Answer → Conclusion (5 elements for 3 marks). For theory: Definition → Formula → Condition/Example (3 distinct blocks). Allocate roughly 1 mark per logical block.

Expected Length

5–8 lines or a 3-step numerical solution

Time Allocation

3–5 minutes

Dos

  • Write GIVEN and REQUIRED at the top before any calculation
  • Show intermediate results (e.g., An before Ae) — each is a potential partial-mark line
  • State which limit state governs in the conclusion
  • Box or underline the final answer
  • Check units at every step (mm² × MPa = N, then convert to kN)

Donts

  • Do not skip the hole-diameter correction for net area
  • Do not assume U = 1.0 without verifying all elements are connected
  • Do not omit the adequacy check (φPn vs. Pu) if the question asks to verify
  • Do not erase correct steps — cross out neatly and write corrections beside them for potential partial credit

Marks

5

Strategy

Use the full GIVEN → REQUIRED → SOLUTION → CONCLUSION structure. For tension members: always show BOTH limit states (yield and rupture), compute each capacity separately, compare, and state which governs. Earn partial credit by writing the correct formula even if arithmetic goes wrong.

Expected Length

12–18 lines with structured steps; full solution with conclusion

Time Allocation

6–8 minutes

General Answer Writing Tips

  • Always write the governing code reference first (e.g., 'Per NSCP 2015 / AISC 360 Section D') before stating any formula — examiners reward code awareness.
  • State BOTH limit states (yielding and rupture) even when only one governs; failing to check both is the single most common reason for zero marks on tension-member problems.
  • Write units at every step of your calculation — a numerical answer without units earns zero in most PRC board rubrics.
  • Box or underline your final answer and include a one-sentence conclusion (e.g., 'Therefore, φPn = 535.7 kN — yielding controls').
  • For net-area problems, draw a quick sketch of the bolt pattern and label the failure path; a labeled sketch earns a diagram mark even if the calculation has a minor arithmetic error.
  • Never use bolt diameter directly in the hole subtraction; add 2 mm (or 3 mm per local practice) for the punching/drilling allowance — examiners specifically check this.
  • When the problem mentions an angle or tee connected through one leg, immediately write U < 1.0 and look up or compute the shear-lag factor before proceeding.
  • Manage time: allocate roughly 1 min per mark. A 5-mark numerical problem should be finished in 5 minutes. If you are stuck, write the formula and partially solved steps — partial credit is available.
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