# 165 ft Round PEB — Member & Material Schedule
## Steel Grade: ASTM A572 Grade 50 (Fy = 345 MPa, Fu = 450 MPa) — LOWEST-WEIGHT OPTIMIZED

> **Optimization note:** Columns **ISMB 400** (lightest SAFE at A572 Gr50). Rafters **ISMB 450** retained (flexural minimum — 90.3% util, cannot go lighter). Total **48.40 t** vs prior **58.49 t (−17%)**, a **−9.10 t** column reduction.
> ISMB 350 alternative noted (46.6 t) but marginal (internal util 88.7%) — **NOT shipped**. A36 alternative at 165-round-peb-a36.

## Geometry
- 165 ft dia, eave 18 ft, apex 26.25 ft, 1:10 cone
- 20 perimeter columns; 4 internal columns @ r = 41.25 ft, h = 22.125 ft, 90° apart
- 20 long rafters (12.637 m) + 4 short rafters (11.424 m)
- 8 ft circular apex ring (torus) — no square inner ring beam
- Purlins Z200×75×1.6 @ 1.5 m c/c — 199 lines, 1,456.7 m

## Member Counts & Tonnage
| Group | Section | Qty | Mass (kg) | Mass (t) |
|---|---|---:|---:|---:|
| Columns (perim 20 + int 4) | ISMB 400 | 24 | 9,078 | 9.08 |
| Rafters (long 20 + short 4) | ISMB 450 | 24 | 25,486 | 25.49 |
| Apex ring torus | CHS 406.4×12.5 | 1 | 935 | 0.93 |
| Purlins | Z200×75×1.6 | 199 | 9,468 | 9.47 |
| Sag rods | 12 mm | — | 1,296 | 1.30 |
| Plates / bolts / cleats | — | 192 | 2,134 | 2.13 |
| **TOTAL** | | | **48,398** | **48.40** |

## Cost @ Rs 285/kg
**PKR 13,794,000  (≈ Rs 13.79 M)**

> Rate editable in the BOQ sheet (Material Takeoff, gold cell C4). Recomputed via formulas.

## Design Checks (AISC 360-22, LRFD)
- **Columns ISMB 400:** internal col Pu≈384 kN, Ly=6.748 m, KL/r=160.7, λc=2.124, φcPn≈646 kN → util **59.4% PASS**. Perimeter **47% PASS**. Web noncompact in compression → ~65% after reduction, still PASS.
- **Rafters ISMB 450:** flexural util ~90.3% (minimum, retained).

## Optimization vs Prior vs ISMB 350
| Scheme | Tonnage | Rate | Cost (PKR) | Remark |
|---|---:|---:|---:|---|
| Prior A572 Gr50 (ISMB 600 cols) | 58.49 t | Rs 285/kg | 16,669,885 | superseded |
| **OPTIMIZED A572 Gr50 (ISMB 400 cols)** | **48.40 t** | Rs 285/kg | **13,794,000** | **THIS ISSUE** |
| ISMB 350 alt (note only) | 46.6 t | Rs 285/kg | 13,281,000 | marginal, NOT shipped |

**Savings:** −10.09 t (−17%) vs prior; **−PKR 2,875,885 (−17.3%)**.

## Exclusions
Sheeting, foundations, erection, paint, transport, 3–5% fabrication wastage.