8.2 Load Weight Calculations for Symmetrical & Composite Shapes

8.2 Load Weight Calculations for Symmetrical & Composite Shapes

Industrial loads rarely arrive as simple, perfect solid rectangles or spheres. On construction sites, chemical plants, refineries, and power generation facilities, riggers routinely encounter composite loads—machinery skids, vessel spools, precast hollow foundation blocks, and fabricated structural trusses composed of multiple interconnected shapes and materials.

To determine the total weight of a composite load, the rigger uses the Principle of Superposition (Decomposition Method):

1. Decompose: Divide the complex structure into simple standard 3D shapes (prisms, cylinders, plates, flanges).
2. Calculate: Determine the volume and weight of each individual positive solid shape.
3. Deduct: Calculate the volume and weight of all negative shapes (hollow cores, cutouts, holes, recesses) and subtract them.
4. Add Contents & Hardware: Add the weight of internal fluids (oil, hydrotest water, catalyst) and structural accessories (flanges, nozzles, lifting lugs).
5. Sum Total: Sum all net components to find the load's net weight.

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1. Worked Example 1: Solid Forged Steel Drive Shaft

+-----------------------------------------------------------------------------------------+
|                      WORKED EXAMPLE 1: SOLID FORGED STEEL SHAFT                         |
+-----------------------------------------------------------------------------------------+
|                 |<--- 1 ft --->|<----------- 10 ft ----------->|<--- 1 ft --->|         |
|                 +--------------+-------------------------------+--------------+         |
|                 | Drive Collar |         Main Shaft Body       | Drive Collar |         |
|                 |  (Dia = 20") |           (Dia = 12")         |  (Dia = 20") |         |
|                 +--------------+-------------------------------+--------------+         |
|                 |<---------------------- Total Length = 12 ft ------------------------>|         |
+-----------------------------------------------------------------------------------------+

Problem Statement

A heavy machinery drivetrain includes a solid forged carbon steel shaft measuring $12\text{ ft}$ overall. It consists of a central shaft body $12\text{ inches}$ ($1.0\text{ ft}$) in diameter and $10\text{ ft}$ long, flanked by two integral end drive collars, each $20\text{ inches}$ in diameter and $1\text{ ft}$ ($12\text{ inches}$) long. Calculate the total steel weight.

Step-by-Step Calculation

1. Component 1: Central Shaft Body ($12\text{"}$ dia $\times 10\text{ ft}$ long):

   • Radius $r = \frac{12\text{ in}}{2} = 6\text{ in} = 0.5\text{ ft}$
   • $\text{Volume } V_1 = \pi \times r^2 \times L = \pi \times (0.5\text{ ft})^2 \times 10\text{ ft} = 3.14159 \times 0.25 \times 10 = 7.854\text{ ft}^3$
   • $\text{Weight } W_1 = 7.854\text{ ft}^3 \times 490\text{ lb/ft}^3 = 3,848.5\text{ lbs}$

2. Components 2 & 3: Two End Collars ($20\text{"}$ dia $\times 1\text{ ft}$ long each):

   • Radius $r = \frac{20\text{ in}}{2} = 10\text{ in} = \frac{10}{12}\text{ ft} = 0.8333\text{ ft}$
   • $\text{Volume per collar } V_c = \pi \times (0.8333\text{ ft})^2 \times 1.0\text{ ft} = 3.14159 \times 0.6944 \times 1.0 = 2.182\text{ ft}^3$
   • Combined Volume $V_{collars} = 2 \times 2.182\text{ ft}^3 = 4.364\text{ ft}^3$
   • Combined Weight $W_{collars} = 4.364\text{ ft}^3 \times 490\text{ lb/ft}^3 = 2,138.4\text{ lbs}$

3. Total Shaft Assembly Weight:

   $$\text{Total Weight} = W_1 + W_{collars} = 3,848.5\text{ lbs} + 2,138.4\text{ lbs} = 5,986.9\text{ lbs} \approx 5,987\text{ lbs}$$

2. Worked Example 2: Concrete Foundation Block with Hollow Core

+-----------------------------------------------------------------------------------------+
|                WORKED EXAMPLE 2: CONCRETE BLOCK WITH HOLLOW CORE VOID                   |
+-----------------------------------------------------------------------------------------+
|                                 <------- 8 ft Width ------->                            |
|                         +------------------------------------------+                    |
|                        /|                                         /|                    |
|                       / |                                        / |                    |
|                      +------------------------------------------+  | 4 ft Height        |
|                      |  |             .-------.                 |  |                    |
|                      |  |           .'         '.               |  |                    |
|                      |  |          /  Void Core  \              |  +                    |
|                      |  |         |  (Dia = 3 ft) |             | /                     |
|                      |  +---------(---------------+-------------|/  10 ft Length        |
|                      |             '.           .'              |                       |
|                      +------------------------------------------+                       |
+-----------------------------------------------------------------------------------------+

Problem Statement

A precast reinforced concrete transformer foundation pad measures $10\text{ ft long} \times 8\text{ ft wide} \times 4\text{ ft high}$. It has a vertical cylindrical cable basement penetration (hollow void) measuring $3\text{ ft in diameter}$ passing completely through its entire $4\text{ ft}$ depth. Calculate the net lifting weight.

Step-by-Step Calculation

1. Solid Gross Envelope Volume ($V_{gross}$):

   $$V_{gross} = L \times W \times H = 10\text{ ft} \times 8\text{ ft} \times 4\text{ ft} = 320.0\text{ ft}^3$$

2. Cylindrical Core Void Volume ($V_{void}$):

   • Void Diameter $d = 3\text{ ft} \implies \text{Radius } r = 1.5\text{ ft}$
   • $V_{void} = \pi \times r^2 \times H = 3.14159 \times (1.5\text{ ft})^2 \times 4\text{ ft} = 3.14159 \times 2.25 \times 4 = 28.274\text{ ft}^3$

3. Net Concrete Volume ($V_{net}$):

   $$V_{net} = V_{gross} - V_{void} = 320.0\text{ ft}^3 - 28.274\text{ ft}^3 = 291.726\text{ ft}^3$$

4. Net Weight (Reinforced Concrete = $150\text{ lb/ft}^3$):

   $$\text{Net Weight} = 291.726\text{ ft}^3 \times 150\text{ lb/ft}^3 = 43,758.9\text{ lbs} \approx 43,760\text{ lbs (21.88 Tons)}$$

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3. Worked Example 3: Steel Pipe Spool with Flanges & Hydrotest Water

+-----------------------------------------------------------------------------------------+
|                  WORKED EXAMPLE 3: FABRICATED PIPE SPOOL WITH WATER                     |
+-----------------------------------------------------------------------------------------+
|        [Flange 1]==================================================[Flange 2]           |
|         (120 lbs)   |<--- 12" Sch 40 Steel Pipe Body (24 ft) ---->|  (120 lbs)          |
|                     |======== FILLED WITH FRESH WATER ===========|                     |
+-----------------------------------------------------------------------------------------+

Problem Statement

A fabricated industrial piping spool is being lifted into a pipe rack following a hydrostatic pressure test without being drained. The spool consists of:

• Pipe Body: $24\text{ ft}$ of $12\text{ inch}$ Nominal Pipe Size (NPS 12) Schedule 40 carbon steel pipe ($OD = 12.75\text{ in} = 1.0625\text{ ft}$; $ID = 11.938\text{ in} = 0.9948\text{ ft}$; Nominal bare pipe weight $= 49.56\text{ lbs/linear ft}$).
• Flanges: Two ANSI Class 300 weld-neck forged steel flanges, each weighing $120\text{ lbs}$.
• Fluid Contents: 100% completely filled with fresh water ($62.4\text{ lb/ft}^3$).

Step-by-Step Calculation

1. Bare Steel Pipe Body Weight ($W_{pipe}$):

   $$W_{pipe} = 24\text{ ft} \times 49.56\text{ lbs/ft} = 1,189.44\text{ lbs}$$

2. Flange Weight ($W_{flanges}$):

   $$W_{flanges} = 2 \times 120\text{ lbs} = 240.0\text{ lbs}$$

3. Internal Water Weight ($W_{water}$):

   • Internal Radius $r_{inner} = \frac{11.938\text{ in}}{2} = 5.969\text{ in} = \frac{5.969}{12}\text{ ft} = 0.4974\text{ ft}$
   • Internal Water Volume $V_{water} = \pi \times (r_{inner})^2 \times L = 3.14159 \times (0.4974\text{ ft})^2 \times 24\text{ ft} = 18.651\text{ ft}^3$
   • Water Weight $W_{water} = 18.651\text{ ft}^3 \times 62.4\text{ lb/ft}^3 = 1,163.82\text{ lbs}$

4. Total Composite Lift Weight:

   $$\text{Total Weight} = W_{pipe} + W_{flanges} + W_{water} = 1,189.44 + 240.0 + 1,163.82 = 2,593.26\text{ lbs} \approx 2,593\text{ lbs}$$

Rigging Insight: Notice that the water inside the pipe ($1,163.8\text{ lbs}$) weighs nearly as much as the steel pipe itself ($1,189.4\text{ lbs}$). Riggers must always verify whether piping and vessels are dry or liquid-filled before rigging!

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4. Worked Example 4: Structural Wide-Flange (I-Beam) Assemblies

+-----------------------------------------------------------------------------------------+
|                    UNDERSTANDING AISC STRUCTURAL BEAM DESIGNATIONS                      |
+-----------------------------------------------------------------------------------------+
|                                 W 14  x  90                                             |
|                                 ----     --                                             |
|                                  |        |                                             |
|                                  |        +---> WEIGHT: 90 lbs per linear foot          |
|                                  +------------> NOMINAL DEPTH: 14 inches                |
+-----------------------------------------------------------------------------------------+

The AISC Beam Designation System

In North American structural steel, wide-flange beams are designated as $W\text{ [Nominal Depth]} \times \text{[Weight per Foot in lbs]}$:

• A $W14 \times 90$ beam is approximately $14\text{ inches}$ deep and weighs $90\text{ lbs per linear foot}$.
• A $W24 \times 162$ beam is approximately $24\text{ inches}$ deep and weighs $162\text{ lbs per linear foot}$.
• A $C12 \times 30$ structural channel weighs $30\text{ lbs per linear foot}$.

Worked Calculation: Structural Skid Grillage

Problem: Calculate the steel weight of a lifting skid frame assembled from:

• Two longitudinal main girder beams: $W14 \times 90$, each $40\text{ ft}$ long.
• Four transverse cross-beams: $W10 \times 39$, each $10\text{ ft}$ long.
• Eight corner gusset plates and connection angles, estimated at $35\text{ lbs}$ each.

Calculation:

• Longitudinal Girders: $2 \times 40\text{ ft} \times 90\text{ lbs/ft} = 7,200\text{ lbs}$
• Transverse Cross-Beams: $4 \times 10\text{ ft} \times 39\text{ lbs/ft} = 1,560\text{ lbs}$
• Hardware / Connection Plates: $8 \times 35\text{ lbs} = 280\text{ lbs}$

$$\text{Total Skid Weight} = 7,200 + 1,560 + 280 = 9,040\text{ lbs}$$

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5. Gross Load vs. Net Load & The Golden Rigger Rule

+-----------------------------------------------------------------------------------------+
|                           CRANE GROSS LOAD CALCULATION                                  |
+-----------------------------------------------------------------------------------------+
|  TOTAL GROSS LOAD ON CRANE =                                                            |
|      Net Object Weight                                                                  |
|    + Internal Liquid / Contents                                                         |
|    + Lifting Beams / Spreader Bars                                                      |
|    + Slings, Shackles, Master Links, Hardware                                           |
|    + Hook Block / Overhaul Ball                                                         |
|    + Effective Hoist Wire Rope Deduction                                               |
+-----------------------------------------------------------------------------------------+

The Golden Rigger Rule

Under all industrial safety standards:

$$\mathbf{\text{“NEVER\ GUESS\ LOAD\ WEIGHT”}}$$

Always verify load weight through one of four approved methods:

1. Certified Shipping Documents / Bill of Lading (BOL)
2. Manufacturer Stamped Equipment Nameplate / Data Sheet
3. Approved Engineering Drawing / Structural Take-Off
4. Geometric Volume & Material Density Calculation (with Verified Scale/Load Cell Pick)