Structural Analysis And Steel Quantity Estimation For A Five-Story Steel Frame

Below is a structural analysis and steel tonnage estimation for the described five-story steel frame structure

---

 

 

 

To perform a meaningful load analysis, the following reasonable assumptions are adopted (typical for light industrial or utility support structures):

Floor dead load (DL): 1.0 kN/m²
(Includes decking, finishes, mechanical/electrical if any, and self-weight of secondary members-primary beam self-weight will be added separately.)

Live load (LL): 2.0 kN/m²
(Typical for light storage or maintenance access; adjust if different usage is intended.)

Roof dead load: 0.8 kN/m²

Roof live load / snow load: 1.0 kN/m²

Wind load: Not distributed per floor here; lateral resistance handled by bracing (analyzed separately).

 

Bay geometry:

Each transverse frame is 1.6 m wide.

Longitudinal spacing between frames: 5 bays → [5.6 m, 5.6 m, 2.8 m, 5.6 m, 5.6 m].

Thus, each "floor panel" supported by main beams has area = 1.6 m × bay width.

Main beams (W10×22) run longitudinally, connecting the 6 transverse frames at each level. Therefore, each beam supports half the tributary width from adjacent bays-but since the structure is only 1.6 m wide total, there are effectively two edge beams supporting the full 1.6 m width (or one central beam with cantilevers). For simplicity, we assume two longitudinal beams, each carrying 0.8 m tributary width.

However, given the narrow width (1.6 m), it is more practical to model the floor system as a single strip where the two longitudinal W10×22 beams act as edge girders supporting a 1.6 m wide platform.

Thus, tributary area per beam per bay = 0.8 m × bay length.

But for column load calculation, we consider the total load per transverse frame.

---

 

Each transverse frame (at a given longitudinal position) supports:

Half the area of the bay to its left + half the area to its right.

For interior frames (Frames 2–5):

Tributary length = (left bay + right bay) / 2

For end frames (Frame 1 and Frame 6):

Tributary length = adjacent bay / 2

Frame #	Left Bay (m)	Right Bay (m)	Tributary Length (m)	Tributary Area per Floor (m²) = 1.6 × Lₜ
1	–	5.6	2.8	4.48
2	5.6	5.6	5.6	8.96
3	5.6	2.8	4.2	6.72
4	2.8	5.6	4.2	6.72
5	5.6	5.6	5.6	8.96
6	5.6	–	2.8	4.48

Note: Total area = (4.48 + 8.96 + 6.72 + 6.72 + 8.96 + 4.48) = 40.32 m²
Full plan area = 1.6 m × 25.2 m = 40.32 m² → ✔️ Consistent.

---

 

 

Dead Load (DL) = 1.0 kN/m²

Live Load (LL) = 2.0 kN/m²

Total unfactored load = 3.0 kN/m²

Frame #	Area (m²)	DL (kN)	LL (kN)	Total Load per Floor (kN)
1,6	4.48	4.48	8.96	13.44
2,5	8.96	8.96	17.92	26.88
3,4	6.72	6.72	13.44	20.16

Additionally, self-weight of main beams must be included in column loads.

W10×22 weight = 32.7 kg/m = 0.321 kN/m

Each frame connects to two beam segments (left and right)

Beam segment lengths = actual bay lengths

Example for Frame 3:

Left bay = 5.6 m → beam weight = 0.321 × 5.6 = 1.80 kN

Right bay = 2.8 m → beam weight = 0.321 × 2.8 = 0.90 kN

Total beam self-weight tributary to Frame 3 ≈ (1.80 + 0.90)/2? → Actually, beam weight is fully supported by columns at ends, so each column at a frame carries half of each adjacent beam's weight.

Thus, additional vertical load from beams per frame per floor: = 0.5 × (left bay + right bay) × 0.321 kN/m

Compute for each frame:

Frame	Adjacent Bays (m)	Total Adjacent Length (m)	Beam Self-Weight (kN)
1	[5.6]	5.6	0.5 × 5.6 × 0.321 = 0.90
2	[5.6, 5.6]	11.2	0.5 × 11.2 × 0.321 = 1.80
3	[5.6, 2.8]	8.4	0.5 × 8.4 × 0.321 = 1.35
4	[2.8, 5.6]	8.4	1.35
5	[5.6, 5.6]	11.2	1.80
6	[5.6]	5.6	0.90

Add this to previous totals:

 

Total vertical load per frame per typical floor (Levels 1–4):

Frame	Area Load (kN)	+ Beam Weight (kN)	Total per Floor (kN)
1,6	13.44	0.90	14.34
2,5	26.88	1.80	28.68
3,4	20.16	1.35	21.51

---

 

 

Roof DL = 0.8 kN/m²

Roof LL = 1.0 kN/m²

Total = 1.8 kN/m²

Area-based roof load per frame:

Frame	Area (m²)	Roof DL (kN)	Roof LL (kN)	Subtotal (kN)
1,6	4.48	3.58	4.48	8.06
2,5	8.96	7.17	8.96	16.13
3,4	6.72	5.38	6.72	12.10

Add same beam self-weight (beams still present at roof):

Total roof load per frame:

Frame	Roof Area Load (kN)	+ Beam Weight (kN)	Total Roof (kN)
1,6	8.06	0.90	8.96
2,5	16.13	1.80	17.93
3,4	12.10	1.35	13.45

---

 

 

Assuming all floors identical (Levels 1–4) and roof as Level 5:

Frame	Load/Floor (kN)	×4 Floors	Roof (kN)	Total Column Load (kN)
1,6	14.34	57.36	8.96	66.3 kN
2,5	28.68	114.72	17.93	132.7 kN
3,4	21.51	86.04	13.45	99.5 kN

Note: These are unfactored service loads. For design, use LRFD combinations (e.g., 1.2DL + 1.6LL).

---

 

 

Gravity loads are transferred from the 1.6 m wide deck to longitudinal W10×22 beams, then to W8×24 columns at each of the 6 frames.

Peak column axial load occurs at Frames 2 and 5 (~133 kN unfactored).

Lateral stability is provided by:

Vertical X-bracing (L3×3×1/4) in at least one bay (e.g., 2.8 m central bay).

Horizontal bracing (C9×20) at roof (and possibly other levels) to diaphragm lateral forces to braced frames.

The structure is statically determinate in gravity, and braced-frame behavior governs lateral response.

Recommendation: Perform a 3D structural analysis (e.g., using SAP2000, ETABS, or STAAD.Pro) to verify member capacities, drift, and connection forces under combined loading per AISC 360 and local building codes.

---

End of analysis.

 

Adaptable regions：Chile, Philippines, New Credonia, Tonga, Virgin Islands, Reunion Island, Peru...

Applications: Structural components for warehousing, Storage, logistics, machinery racking and other special purposes 

Number of stories: 5

Total height: 12.2 m → average story height = 12.2 / 5 ≈ 2.44 m

Building width (short direction): 1.6 m

Building length (long direction): 25.2 m

Frame bays (transverse frames): 6 frames spaced at [5.6 m, 5.6 m, 2.8 m, 5.6 m, 5.6 m] along the 25.2 m length
→ Total bay spacing sum = 5.6 + 5.6 + 2.8 + 5.6 + 5.6 = 25.2 m (consistent)

Primary members:

Columns: W8×24 (per ASTM A992 or equivalent)

Main beams (girders): W10×22

Horizontal bracing: C9×20 (channel section)

Vertical (story) bracing: L3×3×1/4 (equal-leg angle)

 

The structure is a moment-resisting frame laterally stabilized by diagonal bracing in both horizontal and vertical planes.

Gravity Load Path:
Floor loads (dead + live) are transferred via floor system (not detailed here) to main beams (W10×22), then to columns (W8×24). Given the narrow width (1.6 m), it is likely that the main beams span transversely (1.6 m) and are supported by columns aligned along the 25.2 m direction. However, given typical practice and member designation, it is more plausible that:

The main beams run longitudinally (25.2 m direction), supported by transverse frames spaced every ~5–6 m.

But with only 1.6 m width, this suggests a single-bay narrow structure, possibly a bridge, canopy, or equipment support frame.

Given the geometry (1.6 m wide × 25.2 m long × 12.2 m high), this appears to be a linear frame (e.g., a support structure for utilities or a walkway), with 6 transverse frames (each 1.6 m wide) spaced along the 25.2 m length.

Thus:

Each transverse frame consists of two columns (height = 2.44 m per story × 5 = 12.2 m total) and connecting beams at each level.

Main beams (W10×22) likely run longitudinally, connecting the transverse frames at each floor level.

Bracing:

Horizontal bracing (C9×20) at roof and possibly intermediate levels to transfer lateral loads to braced frames.

Vertical (story) bracing (L3×3×1/4) in one or more bays to provide lateral stiffness against wind/seismic loads.

 

 

Unit weights (from AISC Manual):

W8×24: 24 lb/ft = 35.7 kg/m

W10×22: 22 lb/ft = 32.7 kg/m

C9×20: 20 lb/ft = 29.8 kg/m

L3×3×1/4: weight ≈ 4.9 lb/ft = 7.3 kg/m (calculated from area ≈ 1.44 in²)

---

A. Columns

Number of transverse frames: 6

Each frame has 2 columns (assuming rectangular frame)

Total columns = 6 × 2 = 12

Height per column = 12.2 m

Total column length = 12 × 12.2 = 146.4 m

Column steel weight = 146.4 m × 35.7 kg/m ≈ 5,226 kg

 

B. Main Beams (Longitudinal Girders)

Assuming beams at each of the 5 floor levels running the full 25.2 m length, and two beams per level (plus 6 of the 1.6 m width):

Beams per level = 2

Levels = 5

Total beam length = 2 × 5 × 25.2 + 1.6 x 6 x 5 = 300 m

Beam steel weight = 300 m × 32.7 kg/m ≈ 9,810 kg

Note: If the structure uses only one central beam or different configuration, adjust accordingly. This assumes perimeter framing.

 

C. Horizontal Bracing (C9×20)

Typically installed at roof level and possibly at intermediate floors. Assume:

One horizontal bracing layer at roof (plan bracing forming X or single diagonal per panel)

Panels between frames: 5 panels (between 6 frames)

Diagonal length per panel ≈ √(5.6² + 1.6²) ≈ 5.82 m (for 5.6 m bays); for 2.8 m bay: √(2.8² + 1.6²) ≈ 3.22 m

Assume X-bracing in one bay only (minimum for stability), e.g., in the central 2.8 m bay:

Diagonals at roof: 2 × 3.22 = 6.44 m

Possibly also at ground level or intermediate: assume 3 levels with bracing → 3 × 6.44 = 19.3 m

Total C9×20 length ≈ 20 m (conservative)

Weight = 20 m × 29.8 kg/m ≈ 596 kg

If full horizontal trussing is used at every level, quantity increases significantly. This is a minimal estimate. actually there're horizontal bracing in each bay, so the actual usage will be much more.

 

D. Vertical (Story) Bracing (L3×3×1/4)

Assume one braced bay along the length (e.g., between Frame 3 and 4, across the 2.8 m bay) with X-bracing at each story.

Number of stories = 5 → 5 bracing panels

Panel height = 2.44 m, width = 2.8 m

Diagonal length per panel = √(2.44² + 2.8²) ≈ 3.71 m

Two diagonals per panel (X-brace) → 2 × 3.71 = 7.42 m per story

Total length = 5 × 7.42 = 37.1 m

Weight = 37.1 m × 7.3 kg/m ≈ 271 kg

If multiple bays are braced, multiply accordingly.

---

 

 

Component	Weight (kg)
Columns (W8×24)	5,226
Main Beams (W10×22)	9,810
Horizontal Bracing (C9×20)	596
Vertical Bracing (L3×3×1/4)	271
Total (approx.)	15,903 kg

≈ 15.9 metric tons

Note: This excludes connections, base plates, secondary members, or decking. Actual fabrication weight may be 10–15% higher due to connection details and waste.

---

 

 

Slenderness: W8×24 columns (d ≈ 8 in, A ≈ 7.08 in²) over 12.2 m unbraced height may be slender. Effective length factor (K) depends on end conditions. For pinned-pinned, KL/r may exceed limits unless braced. Vertical bracing is essential to reduce effective column length.

Beam Span: W10×22 over 5.6 m (if beams span between frames transversely) is reasonable for light loads. But if beams span 25.2 m continuously, deflection and strength would be inadequate-thus, the assumed configuration (beams as longitudinal girts between transverse frames) is more plausible.

Lateral Stability: Provided by the combination of vertical X-bracing (resisting wind/seismic) and horizontal bracing (diaphragm action).

Load Assumptions: Without specific dead/live/wind loads, this is a preliminary estimate. Detailed design per AISC 360 is required.

---

 

Conclusion
The described steel frame is a narrow, multi-story braced frame with an estimated steel tonnage of approximately 15.9 metric tons. The structural system relies on diagonal bracing for lateral stability, and member sizes appear adequate for light-to-moderate loading, provided proper bracing reduces column effective lengths. A full structural analysis including load combinations, connection design, and serviceability checks is recommended before construction.