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# Section 8.2 Design Data and Formulas

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Section 8.2 contains certain design data, formulas, and charts for the designer. It is not intended to limit design. More detailed design and calculation methods shall be permitted to be used, provided that the stresses and deflections required by other Sections of this Code are not exceeded.

8.2.1 Minimum Rated Load for Passenger Elevators

The following formulas shall be used for determining the minimum rated load of passenger elevators (see also 2.16.1).

8.2.1.1

For an elevator having an inside net platform area of not more than 4.65 m

^{2}(50 ft^{2})*(SI Units)*

*W*= 35A

^{2}+ 325A

*(Imperial Units)*

*W =*0.667A

^{2}

*+ 66.7 A*

8.2.1.2

For an elevator having an inside net platform area of more than 4.65 m

Figure 8.2.1.2 gives the minimum rated loads for various inside net platform areas.

^{2}(50 ft^{2})*(SI Units)*

*W*= 2.45A

^{2}+ 610A - 620

*(Imperial Units)*

*W*= 0.0467A

^{2}+ 125A - 1,367

where

A |
= | inside net platform area, m^{2} (ft^{2}), as specified in Figure 8.2.1.2 |

W |
= | minimum rated load, kg (lb) |

Figure 8.2.1.2 gives the minimum rated loads for various inside net platform areas.

**Figure 8.2.1.2 Minimum Rated Load for Passenger Elevators**

**Figure 8.2.1.2 Minimum Rated Load for Passenger Elevators (Cont'd)**

8.2.2 Electric Elevator Car Frame and Platform Stresses and Deflections

8.2.2.1 General Requirements

The stresses and deflections in side-post-type car frame and platform members shall be based on the data and formulas listed in 8.2.2.

All stresses and their resultant deflections, not only those based on the data and formulas listed in this Section, shall be considered when side-post-type car frames are located off the platform centerline by more than one-eighth of the distance from the front to the back of the platform.

For cars with corner-post, underslung-type, or other special car frame and platform construction, the formulas and specified methods of calculation of loads and the resulting stresses and deflections do not generally apply and shall be modified to suit the specific conditions and requirements in each case.

The maximum allowable stresses and deflections of members of all car frames and platforms shall be not more than those permitted by 2.15.10 and 2.15.11.

8.2.2.1.1 Formula Symbols

The symbols used in the formulas in 8.2.2 shall have the following meaning:

A | = | net area of section, m^{2} (in.^{2}) |

B | = | inside clear width of car, mm (in.) |

C | = | net weight of complete elevator car, kg (lb) |

D | = | distance between guide rails, mm (in.) |

E | = | modulus of elasticity of material used, MPa (psi) |

G | = | load supported by crosshead with the maximum load for the class of loading in the car at rest at the top terminal landing, kg (lb) |

H | = | vertical center distance between upper and lower guide shoes (or rollers), mm (in.) |

I | = | moment of inertia of member, gross section, mm^{4} (in.^{4}) |

K | = | turning moment as determined by class of loading, N-mm (lbf-in.) |

L | = | free length of uprights (distance from lowest fastening in crosshead to top fastening in plank), mm (in.) |

R | = | least radius of gyration of section, mm (in.) |

W | = | rated load, kg (lb) |

Z | = | combined section moduli of plank members, gross section, mm^{3} (in.^{3}) |

Z_{u} | = | section modulus of one upright, gross section, mm^{3} (in.^{3}) |

8.2.2.2 Car Frame Crosshead

The stresses in the car frame crosshead shall be based on the total load supported by the crosshead with the car and the maximum load for the class of loading in the car when at rest at the top terminal landing.

8.2.2.3 Car Frame Plank (Normal)

The stresses in the car frame plank when the stringers are supported directly on the plank members shall be based on the sum of five-eighths of the platform weight uniformly distributed plus the concentrated loads due to the tension in the compensation means and the traveling cables with the car at the top of its travel plus the loading specified in (a) or (b).

*(a)*For passenger and Class A freight loading, five-eighths of the rated load uniformly distributed.

*(b)*For Class B and Class C freight loading, the loading as specified in 8.2.2.6.

8.2.2.4 Car Frame Plank (Buffer Engagement)

In calculating the stress resulting from oil buffer or elastomeric buffer engagement, one-half the sum of the weight of the car and its rated load shall be considered as being concentrated at each end of the plank with the buffer force applied at the middle. The buffer force shall be considered to be that required to produce gravity retardation with rated load in the car.

The following formula shall be used to determine the stress resulting from buffer engagement:

*(SI Units)*

*(Imperial Units)*

Where more than one buffer is used, the formula shall be modified to suit the location of the buffers.

NOTE (8.2.2.4): Symbols used in the preceding formula are defined in 8.2.2.1.1.

8.2.2.5 Car Frame Uprights (Stiles)

8.2.2.5.1 Stress Due to Bending and Tension

*(SI Units)*

*(Imperial Units)*

where

KL/4HZ_{U} |
= | the bending stress in each upright in the plane of the frame due to live load W on the platform for the class of loading (A, B, or C) for which the elevator is to be used (see 2.16.2.2) |

G/2A |
= | the tensile strength in each upright and K is determined by the following formulas (see Figure 8.2.2.5.1): |

*(a)*For Class A freight loading or passenger loading

*(SI Units)*

*(Imperial Units)*

*(b)*For Class B freight loading

*(SI Units)*

whichever is greater.

*(Imperial Units)*

whichever is greater.

*(c)*For Class C freight loading

*(SI Units)*

*(Imperial Units)*

NOTE (8.2.2.5.1): Symbols used in the preceding formulas are defined in 8.2.2.1.1.

8.2.2.5.2 Slenderness Ratio

The slenderness ratio

*L/R*for uprights subject to compressions other than those resulting from safety and buffer action shall not exceed 120. Where the upper side-brace connections on passenger elevator car frame uprights are located at a point less than two-thirds of*L*from the bottom (top fastening in the car frame plank), a slenderness ratio of*L/R*not exceeding 160 is permissible (*L/R*≤ 160).NOTE (8.2.2.5.2): Symbols used in the above formulas are defined in 8.2.2.1.1.

8.2.2.5.3 Moment of Inertia

The moment of inertia of each upright shall be not less than determined by the following formula:

*(SI Units)*

*(Imperial Units)*

NOTE (8.2.2.5.3): Symbols used in the preceding formula are defined in 8.2.2.1.1.

8.2.2.6 Freight Elevator Platform

The calculation for stresses in the platform members of freight elevators shall be based on the following concentrated loads assumed to occupy the position that will produce the maximum stress:

*(a)*for Class A loading, 25% of the rated load

*(b)*for Class B loading, 75% of the rated load or 15 400 kg (34,000 lb), whichever is less, divided into two equal parts 1525 mm (60 in.) apart

*(c)*for Class C1 loading, with a load rating of 9000 kg (20,000 lb) or less, 80% of the rated load divided into two equal parts, 765 mm (30 in.) apart

*(d)*for Class C2 loading, with a load rating of 9000 kg (20,000 lb) or less, 80% of the rated load or of the loaded truck weight, whichever is greater, divided into two equal parts, 765 mm (30 in.) apart

*(e)*for Class C1 or Class C2 loading, with a rated load in excess of 9000 kg (20,000 lb), 80% of the 9000 kg (20,000 lb) or of the maximum loaded truck weight, whichever is greater, divided into two equal parts, 765 mm (30 in.) apart

*(f)*for Class C3 loading, determined on the basis of the actual loading conditions but not less than that required for Class A loading

**Figure 8.2.2.5.1 Turning Moment Based on Class of Loading**

GENERAL NOTE See 8.2.2.5.1 for formulas in SI units.

8.2.2.7 Hoisting Rope Hitch Plates and Shapes

The stresses in hoisting rope hitch plates and shapes shall be based on the total applied rope load with the car and its rated load at rest at the top terminal landing.

8.2.3 Impact on Buffer Supports

8.2.3.1 Buffer Reaction and Impact for Oil Buffer and Elastomeric Buffer Supports

8.2.3.2 Buffer Reaction and Impact for Spring Buffer Supports

The following formulas give the buffer reaction and the impact on the supports of car and counterweight spring buffers that do not fully compress under the conditions outlined in 2.1.2.3(a):

*(a) Buffer Reaction*

*(SI Units)*

*(Imperial Units)*

*(b) Impact*

*P = R*

where

P | = | impact, N (lbf) |

R | = | buffer reaction, N (lbf) |

S | = | buffer stroke, m (ft) |

V | = | speed at impact (for electric), m/s (ft/s); operating speed in the down direction (for hydraulic), m/s (ft/s) |

W | = | weight of the car plus rated load or weight of the counterweight, kg (lb) |

8.2.4 Gravity Stopping Distances

The following formula gives the value of the stopping distance based on gravity retardation from any initial velocity (see 2.4.6, 2.4.8, 2.4.9, and 2.22.4.1):

*(SI Units)*

*S =*51

*V*

^{2}

*(Imperial Units)*

where

S |
= | free fall (gravity stopping distance), mm (in.) |

V |
= | initial velocity, m/s (ft/min) |

Figure 8.2.4 shows the gravity stopping distances from various initial velocities.

Figure 8.2.4 Gravity Stopping Distances

Figure 8.2.4 Gravity Stopping Distances

8.2.5 Governor Tripping Speeds

Figure 8.2.5 gives the maximum governor tripping speeds for various rated speeds (see 2.18.2.1).

Figure 8.2.5 Maximum Governor Tripping SpeedsFigure 8.2.5 Maximum Governor Tripping Speeds

**Figure 8.2.5 Maximum Governor Tripping Speeds (Cont'd)**

8.2.6 Stopping Distances for Car and Counterweight Safeties

The following formulas shall be used to determine the maximum and minimum stopping distances for Type B car and counterweight safeties (see 2.17.3):

*(SI Units)*

*(Imperial Units)*

where

S |
= | maximum stopping distance, m (ft) |

S' |
= | minimum stopping distance, m (ft) |

V |
= | governor tripping speed, m/s (ft/min) |

Figure 8.2.6 shows the maximum and minimum stopping distances from various governor tripping speeds.

Figure 8.2.6 Stopping Distances for Type B Car and Counterweight Safeties

Figure 8.2.6 Stopping Distances for Type B Car and Counterweight Safeties

**Figure 8.2.6 Stopping Distances for Type B Car and Counterweight Safeties (Cont'd)**

**Figure 8.2.6 Stopping Distances for Type B Car and Counterweight Safeties (Cont'd)**

8.2.7 Factors of Safety for Suspension Wire Ropes for Power Elevators

Figure 8.2.7 shows the minimum factors of safety for suspension wire ropes of power elevators for various rope speeds (see 2.20.3).

8.2.8 Hydraulic Jack and Piping

8.2.8.1 Plunger Design

8.2.8.1.1 Plungers Not Subject to Eccentric Loading

*(a)*Where the slenderness ratio of the plunger is less than 120

*(SI Units)*

*(Imperial Units)*

*(b)*Where the slenderness ratio of the plunger is greater than 120

*(SI Units)*

*(Imperial Units)*

Formulas are for steel where

A |
= | net sectional area of plunger (area of metal), m^{2} (in.^{2}) |

L |
= | maximum free length of plunger, mm (in.). Where a plunger-follower guide conforming to 3.18.2.7 is used, L shall be taken as one-half the amount that the free length would be if no follower guide were provided. |

R |
= | radius of gyration of plunger section, mm (in.) |

W |
= | allowable gross weight to be sustained by the plunger, N (lbf). Where a counterweight is provided, the weight of the counterweight plus the unbalanced weight of the counterweight ropes shall be permitted to be deducted in determining W. In determining W, one-half of the weight of the plunger shall be included except where a plunger-follower guide conforming to 3.18.2.7 is used, in which case, three-fourths of the plunger weight shall be included. |

W/A |
= | fiber stress, kPa (psi] |

Figure 8.2.8.1.1 Allowable Gross Loads

Figure 8.2.8.1.1 Allowable Gross Loads

**Figure 8.2.8.1.1 Allowable Gross Loads (Cont'd)**

NOTE [8.2.8.1.1(a) and 8.2.8.1.1(b)]: Figure 8.2.8.1.1 has been calculated from the formulas given in 8.2.8.1.1 for the more usual pipe sizes and pipe schedules and indicates allowable gross loads directly.

*(c)*Plungers having a free length of 7.6 m (25 ft) or less shall be permitted to be accepted without further examination for strength and elastic stability, provided all of the following conditions exist:

*(1)*the working pressure is 2070 kPa (300 psi) or less

*(2)*the plunger is 100 mm (4 in.) nominal pipe size or larger

*(3)*pipe not lighter than Schedule 40 is used, and not more than 1.6 mm (0.063 in.) of metal has been removed from the wall thickness in machining

*(d) Plungers With Varying Cross Section.*For plungers with varying cross section, the stress shall be calculated for a factor of safety of at least 3 using accepted methods for elastic stability.

GENERAL NOTES:

- Curves are based on the removal of not more than 1.5 mm (0.0625 in.) from the wall thickness in machining.
- Curves stop at 18 m (59 ft) for convenience only. For plunger sizes or lengths not shown on this chart, see the applicable formula in 8.2.8.1.1,

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