> ## Content Index > Fetch the complete content index at: https://milepointindex.com/llms.txt > Use this file to discover other available public pages before exploring further. # Can Carbon Fiber Save a Splitting Timber Bridge? - URL: https://milepointindex.com/2026-11-07_sr-285-bridge/ - Published: 2026-11-07T20:16:26.000Z - Updated: 2026-11-07T20:19:29.000Z - Description: Broadwater County, Montana added 1,162 residents between 2010 and 2020, a 20.7 percent climb, and the corridor's busiest recorded segment now carries 4,902 vehicles per day. The National Bridge Inventory lists 4… - Author: Mile Point Index - Tags: Case File, Field Briefing *MILE POINT INDEX · CASE FILE & FIELD BRIEFING · November 7, 2026* FREE SAMPLE LESSON PACKET & CASE FILE This complete Case File and 8-page Classroom Packet, including the Research Highlight Bulletin, Instructor Lesson Plan, Student Worksheet, and Worked Answer Key, is unlocked for public evaluation and immediate classroom use ($79/yr Solo · $299/yr Department). [Download Full 8-Page PDF Packet](https://milepointindex.com/content/files/2026/11/MPI%5FEp01%5FComplete%5FClassroom%5FKit-11.pdf)[View Department & Solo Licensing](https://milepointindex.com/licensing/) ## 01 // The Incident & Field Setup Broadwater County, Montana added 1,162 residents between 2010 and 2020, a 20.7 percent climb, and the corridor's busiest recorded segment now carries 4,902 vehicles per day. The National Bridge Inventory lists 4 bridges within five miles, 1 of them rated poor. **The Challenge.** Broadwater County grew from 5,612 residents in 2010 to 6,774 in 2020, and peak traffic on S285 near Toston reaches 4,902 vehicles a day. Of four bridges within five miles, one is Poor and three are Fair, all fifty years old or more. A split girder means weight limits, closure, or emergency replacement. The study tested whether allowable-stress equations, plus a perfect-bond assumption for the retrofit, predict capacity. **The Research.** The team salvaged twenty-two Douglas-fir and larch girders, six by eighteen and eight by eighteen inches, some split, some cracked, some sound. Coupons of the glass channels and carbon-glass strips were pulled to failure first. Beams were then tested in four-point bending, set up for shear and for flexure, with string potentiometers, a load cell, an extensometer, bearing plates, lateral bracing, and calipers. **Key Findings.** The verdict was conservative: every beam carried more than its calculated capacity. Glass channels added 11.3% and 23.1% shear on narrow beams, 11.5% and 48.5% on wide. Carbon-glass crack repair raised moment capacity 29.9% and 50.5%. A six-foot channel restored narrow split beams to 97.1% of control and wide beams reached 112.2%. Installation took 1.5 hours and 30 minutes; seven months later, nothing showed. **Engineering Impact.** Designers should match the repair to the damage: carbon-glass for broken or badly cracked girders, strips alone for minor cracks. Treat allowable-stress predictions as conservative, not exact. Specifications need surface preparation, strip end anchorage, confinement, and cure time for cold mornings. Inspectors should tap the channels, check strip ends for moisture, and keep monitoring, since fatigue, freeze-thaw, and long-term durability remain unproven. ## 02 // Printable Classroom & Briefing Packet (PDF Downloads) Print ready on Letter stock. Take the eight-page kit, the one-page research highlight bulletin, or the single handout a class needs. Mile Point Index // Classroom Kit // Episode 01 8 printable pages, Letter size White background, black ink, three report field photos on page one. [Download Complete Classroom Kit (8-Page PDF)Highlight sheet, lesson plan, worksheet, and key](https://milepointindex.com/content/files/2026/11/MPI%5FEp01%5FComplete%5FClassroom%5FKit-11.pdf)[Download Research Highlight Fact Sheet (1-Page PDF)Four blocks, three field photos, QR](https://milepointindex.com/content/files/2026/11/MPI%5FEp01%5FResearch%5FHighlight%5FSheet-5.pdf)[Download Student Worksheet Only (2-Page PDF)Google Classroom ready](https://milepointindex.com/content/files/2026/11/MPI%5FEp01%5FStudent%5FWorksheet-10.pdf)[Download Instructor Lesson Plan & Pacing Guide (2-Page PDF)Standards, pacing, pause points](https://milepointindex.com/content/files/2026/11/MPI%5FEp01%5FInstructor%5FLesson%5FPlan-10.pdf)[Download Worked Answer Key & Grading Rubric (3-Page PDF)Solutions and rubric](https://milepointindex.com/content/files/2026/11/MPI%5FEp01%5FAnswer%5FKey-10.pdf) ## 03 // Quick-Reference Telemetry, Video Pause Points & Collapsible Answer Key **Video pause points.** Keep this list beside the player. - **01:44** Part 1: The everyday question - **02:45** Part 2: The field test - **06:15** Part 3: Where it's happening on the ground - **08:04** Part 4: What comes next **Design against measured.** Both unit systems. | Parameter | Design baseline | Measured in field | Engineering takeaway | | ---------------------------------------------- | ----------------------------------------- | -------------------------------------- | ------------------------------------------------------------ | | **Shear gain, strengthened 6x18 beam** | Control shear capacity, 100% | +23.1% with GFRP channels | Channels add shear capacity to sound girders. | | **Shear gain, strengthened 8x18 beam** | Control shear capacity, 100% | +48.5% with GFRP channels | Wider girder gained more from channels. | | **Moment gain, C-S crack repair 8x18** | Control moment capacity, 100% | +50.5% after C-S repair | C-S suits severe cracking and broken girders. | | **Strip-only strengthening, 8x18 moment** | Control moment capacity, 100% | +140.0% over controls | Inflated by an underperformed control; treat as upper bound. | | **Split repair flexure, 6x18 beam** | Restore full control capacity | 97.1% of control capacity | Near full restoration; check remaining margin. | | **Calculated versus measured moment capacity** | Allowable-stress, perfect-bond prediction | Every tested beam exceeded calculation | Method is conservative, not exact. | | **Field installation time, two bridges** | Heavy sister-girder repair, long closure | 1.5 hours and 30 minutes | Standard tools allow short traffic disruption. | | **Seven-month follow-up inspection result** | Long-term durability assumed | No visible deterioration or issues | Visual only; fatigue and weathering unproven. | **Worksheet questions.** Five problems from the record above. 1. The salvaged test girders (main beams supporting the deck) were 6 in x 18 in and 8 in x 18 in. Using 1 in = 25.4 mm, find each cross-sectional area. Peak shear stress (sliding stress between internal wood layers) in a rectangular beam is proportional to V/A. Under the same shear force V, what is the ratio of peak shear stress in the 8 in beam to the 6 in beam? 2. For the same 6 in x 18 in and 8 in x 18 in girders, use 1 in = 25.4 mm and 1 kip-ft = 1.3558 kN-m. Compute each section modulus (shape's resistance to bending stress) for a rectangle. If bending stress (stretch or squeeze stress from bending) limits both controls equally, how much more moment can the 8 in control carry than the 6 in control? 3. A split (lengthwise crack running along the grain) repair using full-length GFRP channels (glass-fiber U-sections fastened along the girder) restored 6 in x 18 in beams to 97.1 percent of control moment capacity (largest bending moment before failure) and brought 8 in x 18 in beams to 112.2 percent. Each control has factor of safety (capacity divided by the applied demand) FS\_c. Using 1 in = 25.4 mm and 1 kip-ft = 1.3558 kN-m, find each repaired factor of safety and the repaired 8 in to 6 in capacity ratio. 4. Channel strengthening raised shear capacity (largest shear force before the beam fails) by 23.1 percent for undamaged 6 in x 18 in girders and 48.5 percent for 8 in x 18 in girders. Assume each control's shear capacity scales with cross-sectional area. Using 1 in = 25.4 mm and 1 kip = 4.448 kN, find the share of strengthened capacity carried by the GFRP channels (glass-fiber U-sections fastened along the girder) and the strengthened 8 in to 6 in capacity ratio. 5. Strip-only (bonded strips without a channel) strengthening raised 8 in x 18 in moment capacity (largest bending moment before failure) by 140.0 percent, but its control underperformed; C-S (channels and strips used together) strengthening gave 45.0 percent. Field installs took 1.5 hours and 30 minutes, and inspection covered seven months on girders more than 80 years old. Using 1 kip-ft = 1.3558 kN-m, 1 hour = 60 minutes, 1 minute = 60 seconds, and 1 year = 12 months, decide which gain to design on and what to monitor next. Click to Reveal Instructor Answer Key & Worked Math **Problem 1.** 1. Convert with 1 in = 25.4 mm: b6 = 6 in x 25.4 mm/in = 152.4 mm, b8 = 8 in x 25.4 mm/in = 203.2 mm, and h = 18 in x 25.4 mm/in = 457.2 mm. 2. A6 = b x h = 6 in x 18 in = 108 in²; applying (25.4 mm/in)² = 645.16 mm²/in² gives 108 in² x 645.16 mm²/in² = 69,677 mm², matching 152.4 mm x 457.2 mm. 3. A8 = 8 in x 18 in = 144 in²; applying 645.16 mm²/in² gives 144 in² x 645.16 mm²/in² = 92,903 mm², matching 203.2 mm x 457.2 mm. 4. At equal V, τ8 / τ6 = A6 / A8 = 108 in² / 144 in² = 0.750, and in SI 69,677 mm² / 92,903 mm² = 0.750, so the 8 in (203.2 mm) girder sees 25.0 percent less peak shear stress. **Problem 2.** 1. Convert with 1 in = 25.4 mm: 6 in x 25.4 mm/in = 152.4 mm, 8 in x 25.4 mm/in = 203.2 mm, and 18 in x 25.4 mm/in = 457.2 mm. 2. S6 = b h² / 6 = 6 in x (18 in)² / 6 = 324 in³; applying (25.4 mm/in)³ = 16,387 mm³/in³ gives 324 in³ x 16,387 mm³/in³ = 5.309 x 10^6 mm³, matching 152.4 mm x (457.2 mm)² / 6. 3. S8 = 8 in x (18 in)² / 6 = 432 in³; applying 16,387 mm³/in³ gives 432 in³ x 16,387 mm³/in³ = 7.079 x 10^6 mm³, matching 203.2 mm x (457.2 mm)² / 6. 4. At equal limiting stress σ = M / S, M8 / M6 = S8 / S6 = 432 in³ / 324 in³ = 1.333, and in SI 7.079 x 10^6 mm³ / 5.309 x 10^6 mm³ = 1.333. 5. So M8 = 1.333 M6 in kip-ft; multiplying both moments by 1.3558 kN-m per kip-ft gives M8 = 1.333 M6 in kN-m, a 33.3 percent larger moment for the 8 in (203.2 mm) control. **Problem 3.** 1. Capacity ratio r = M\_repaired / M\_control: r6 = 0.971 and r8 = 1.122; converting both moments by 1.3558 kN-m per kip-ft leaves r6 = 0.971 and r8 = 1.122 in kN-m as well. 2. FS\_r = capacity / demand = r x FS\_c with demand unchanged: FS\_r6 = 0.971 FS\_c and FS\_r8 = 1.122 FS\_c, whether demand and capacity are both in kip-ft or both in kN-m. 3. Margin check: FS\_r6 of at least 1.000 requires FS\_c of at least 1 / 0.971 = 1.030 in kip-ft or kN-m terms, while the 8 in repair raises margin by 1.122 - 1.000 = 0.122, or 12.2 percent. 4. Control moment ratio from section shape: 8 in x 25.4 mm/in = 203.2 mm and 6 in x 25.4 mm/in = 152.4 mm at equal 18 in (457.2 mm) depth, so M\_c8 / M\_c6 = 8 in / 6 in = 1.333 and 203.2 mm / 152.4 mm = 1.333. 5. Repaired capacity ratio = 1.333 x (1.122 / 0.971) = 1.333 x 1.156 = 1.541, so the repaired 8 in (203.2 mm) girder carries about 1.541 times the moment of the repaired 6 in (152.4 mm) girder in kip-ft or kN-m. **Problem 4.** 1. Strengthened capacity V\_s = (1 + gain) x V\_c: V\_s6 = 1.231 V\_c6 and V\_s8 = 1.485 V\_c8 in kip; multiplying both sides by 4.448 kN/kip gives the same 1.231 and 1.485 factors in kN. 2. Channel share = gain / (1 + gain): 0.231 / 1.231 = 0.188 (18.8 percent) for the 6 in girder and 0.485 / 1.485 = 0.327 (32.7 percent) for the 8 in girder, identical in kip and in kN after the 4.448 kN/kip factor. 3. Control ratio from area: A8 = 8 in x 18 in = 144 in² and A6 = 6 in x 18 in = 108 in²; applying 645.16 mm²/in² gives 92,903 mm² and 69,677 mm², so V\_c8 / V\_c6 = 144 / 108 = 1.333 and 92,903 / 69,677 = 1.333. 4. Strengthened ratio V\_s8 / V\_s6 = 1.333 x 1.485 / 1.231 = 1.608 in kip or kN, so the strengthened 8 in (8 in x 25.4 mm/in = 203.2 mm) girder carries about 1.608 times the shear of the strengthened 6 in (152.4 mm) girder. **Problem 5.** 1. Capacity factor = 1 + gain: strip-only 1 + 1.400 = 2.400 M\_c and C-S 1 + 0.450 = 1.450 M\_c in kip-ft; multiplying by 1.3558 kN-m per kip-ft keeps 2.400 M\_c and 1.450 M\_c in kN-m, and 2.400 rests on a weak control. 2. Install time: 1.5 h x 60 min/h = 90 min, then 90 min x 60 s/min = 5,400 s, versus 30 min x 60 s/min = 1,800 s; ratio 90 min / 30 min = 5,400 s / 1,800 s = 3.0 for the broken-girder C-S job. 3. Evidence window: 80 years x 12 months/year = 960 months, so 7 months / 960 months = 0.0073 (0.73 percent) of girder age and less than one 12-month seasonal cycle. 4. Decision: design on the 1.450 C-S factor in kip-ft or kN-m for broken or severely cracked girders, use strip-only for minor cracks, and monitor deflection, bond lines, fasteners, moisture, and fatigue (weakening from many repeated load cycles) for several seasons. 1. Convert with 1 in = 25.4 mm: b6 = 6 in x 25.4 mm/in = 152.4 mm, b8 = 8 in x 25.4 mm/in = 203.2 mm, and h = 18 in x 25.4 mm/in = 457.2 mm. 2. A6 = b x h = 6 in x 18 in = 108 in²; applying (25.4 mm/in)² = 645.16 mm²/in² gives 108 in² x 645.16 mm²/in² = 69,677 mm², matching 152.4 mm x 457.2 mm. 3. A8 = 8 in x 18 in = 144 in²; applying 645.16 mm²/in² gives 144 in² x 645.16 mm²/in² = 92,903 mm², matching 203.2 mm x 457.2 mm. 4. At equal V, τ8 / τ6 = A6 / A8 = 108 in² / 144 in² = 0.750, and in SI 69,677 mm² / 92,903 mm² = 0.750, so the 8 in (203.2 mm) girder sees 25.0 percent less peak shear stress. **Problem 2.** 1. Convert with 1 in = 25.4 mm: 6 in x 25.4 mm/in = 152.4 mm, 8 in x 25.4 mm/in = 203.2 mm, and 18 in x 25.4 mm/in = 457.2 mm. 2. S6 = b h² / 6 = 6 in x (18 in)² / 6 = 324 in³; applying (25.4 mm/in)³ = 16,387 mm³/in³ gives 324 in³ x 16,387 mm³/in³ = 5.309 x 10^6 mm³, matching 152.4 mm x (457.2 mm)² / 6. 3. S8 = 8 in x (18 in)² / 6 = 432 in³; applying 16,387 mm³/in³ gives 432 in³ x 16,387 mm³/in³ = 7.079 x 10^6 mm³, matching 203.2 mm x (457.2 mm)² / 6. 4. At equal limiting stress σ = M / S, M8 / M6 = S8 / S6 = 432 in³ / 324 in³ = 1.333, and in SI 7.079 x 10^6 mm³ / 5.309 x 10^6 mm³ = 1.333. 5. So M8 = 1.333 M6 in kip-ft; multiplying both moments by 1.3558 kN-m per kip-ft gives M8 = 1.333 M6 in kN-m, a 33.3 percent larger moment for the 8 in (203.2 mm) control. **Problem 3.** 1. Capacity ratio r = M\_repaired / M\_control: r6 = 0.971 and r8 = 1.122; converting both moments by 1.3558 kN-m per kip-ft leaves r6 = 0.971 and r8 = 1.122 in kN-m as well. 2. FS\_r = capacity / demand = r x FS\_c with demand unchanged: FS\_r6 = 0.971 FS\_c and FS\_r8 = 1.122 FS\_c, whether demand and capacity are both in kip-ft or both in kN-m. 3. Margin check: FS\_r6 of at least 1.000 requires FS\_c of at least 1 / 0.971 = 1.030 in kip-ft or kN-m terms, while the 8 in repair raises margin by 1.122 - 1.000 = 0.122, or 12.2 percent. 4. Control moment ratio from section shape: 8 in x 25.4 mm/in = 203.2 mm and 6 in x 25.4 mm/in = 152.4 mm at equal 18 in (457.2 mm) depth, so M\_c8 / M\_c6 = 8 in / 6 in = 1.333 and 203.2 mm / 152.4 mm = 1.333. 5. Repaired capacity ratio = 1.333 x (1.122 / 0.971) = 1.333 x 1.156 = 1.541, so the repaired 8 in (203.2 mm) girder carries about 1.541 times the moment of the repaired 6 in (152.4 mm) girder in kip-ft or kN-m. **Problem 4.** 1. Strengthened capacity V\_s = (1 + gain) x V\_c: V\_s6 = 1.231 V\_c6 and V\_s8 = 1.485 V\_c8 in kip; multiplying both sides by 4.448 kN/kip gives the same 1.231 and 1.485 factors in kN. 2. Channel share = gain / (1 + gain): 0.231 / 1.231 = 0.188 (18.8 percent) for the 6 in girder and 0.485 / 1.485 = 0.327 (32.7 percent) for the 8 in girder, identical in kip and in kN after the 4.448 kN/kip factor. 3. Control ratio from area: A8 = 8 in x 18 in = 144 in² and A6 = 6 in x 18 in = 108 in²; applying 645.16 mm²/in² gives 92,903 mm² and 69,677 mm², so V\_c8 / V\_c6 = 144 / 108 = 1.333 and 92,903 / 69,677 = 1.333. 4. Strengthened ratio V\_s8 / V\_s6 = 1.333 x 1.485 / 1.231 = 1.608 in kip or kN, so the strengthened 8 in (8 in x 25.4 mm/in = 203.2 mm) girder carries about 1.608 times the shear of the strengthened 6 in (152.4 mm) girder. **Problem 5.** 1. Capacity factor = 1 + gain: strip-only 1 + 1.400 = 2.400 M\_c and C-S 1 + 0.450 = 1.450 M\_c in kip-ft; multiplying by 1.3558 kN-m per kip-ft keeps 2.400 M\_c and 1.450 M\_c in kN-m, and 2.400 rests on a weak control. 2. Install time: 1.5 h x 60 min/h = 90 min, then 90 min x 60 s/min = 5,400 s, versus 30 min x 60 s/min = 1,800 s; ratio 90 min / 30 min = 5,400 s / 1,800 s = 3.0 for the broken-girder C-S job. 3. Evidence window: 80 years x 12 months/year = 960 months, so 7 months / 960 months = 0.0073 (0.73 percent) of girder age and less than one 12-month seasonal cycle. 4. Decision: design on the 1.450 C-S factor in kip-ft or kN-m for broken or severely cracked girders, use strip-only for minor cracks, and monitor deflection, bond lines, fasteners, moisture, and fatigue (weakening from many repeated load cycles) for several seasons. ## 04 // Primary Source & Public Data Ledger Every number traces to a public record. ### Study report **Use of Fiber-Reinforced Polymer Composites for Bridge Repairs in Montana** [Read the full report (PDF)](https://rosap.ntl.bts.gov/view/dot/89574/dot%5F89574%5FDS1.pdf?ref=milepointindex.com) | [DOI 10.21949/1529573](https://doi.org/10.21949/1529573?ref=milepointindex.com) ### Bridge inventory (FHWA NBI) Structure numbers carried by S285: `S0028500209001` (S 285 over TOSTON CANAL, rated poor), `S0028500604001` (S 285 over CROW CREEK). Searchable at [InfoBridge](https://infobridge.fhwa.dot.gov/?ref=milepointindex.com). ### Traffic (FHWA HPMS) The busiest recorded segment on this corridor carries 4,902 vehicles per day, read from the federal Highway Performance Monitoring System at the study crossing. [HPMS documentation](https://www.fhwa.dot.gov/policyinformation/hpms.cfm?ref=milepointindex.com) ### Crash records (NHTSA FARS) Federal records count no fatal-involved crashes within five miles of the study crossing. [FARS documentation and downloads](https://www.nhtsa.gov/research-data/fatality-analysis-reporting-system-fars?ref=milepointindex.com) ### Federal obligations (USAspending) 1 obligated projects on this route. Awards: [socrata-g43q-hx7i-2466c603d9567651](https://www.usaspending.gov/award/socrata-g43q-hx7i-2466c603d9567651?ref=milepointindex.com).