A temporary elevator is assembled at the construction site to raise building materials, such as cement, to a height of 20 m. It is estimated that the maximum weight of the material to be raised is 5 kN. It is observed that the acceleration in such applications is 1 m/s^2. 10 mm diameter,

Question

A temporary elevator is assembled at the construction site to raise building materials, such as cement, to a height of 20 m. It is estimated that the maximum weight of the material to be raised is 5 kN. It is observed that the acceleration in such applications is 1 m/s². 10 mm diameter, 6 × 19 construction wire ropes with fibre core are used for this application. The tensile designation of the wire is 1570 and the factor of safety should be 10 for preliminary calculations. Determine the number of wire ropes required for this application. Neglect bending stresses.

Accepted Answer

[latex] ext { Given } \quad W=5 kN \quad h=20 m \quad \alpha=1 m / s ^{2} [/latex].

For wire rope, construction = 6 × 19

[latex] d_{r}=10 mm \quad ext { tensile designation }=1570 \quad(f s)=10 [/latex].

Let us assume that the number of wire ropes is z. The force acting on each wire rope comprises the following factors:

(i) the weight of the material to be raised;
(ii) the weight of the wire rope; and
(iii) the force due to acceleration of the material and the wire rope.
Step I Weight of the material
The weight of the material raised by each wire rope is given by,

[latex] \left(\frac{5000}{z} ight) N [/latex] (i).

Step II Weight of the wire rope
From Table 23.4, the mass of 100 m long wire rope is 34.6 kg. Since the height is 20 m, the weight of the wire is given by,

Table 23.4 Breaking load and mass for 6 × 19 (12/6/1) construction wire ropes with fibre core

Minimum breaking load corresponding to tensile designation of (kN)						Approximate mass (kg/100 m)		Nominal diameter [latex]\left(d_{r} ight)[/latex] (mm)
1960		1770		1570		Approximate mass (kg/100 m)
Steel core	Fibre core	Steel core	Fibre core	Steel core	Fibre core	Steel core	Fibre core
41.6	39	37.6	35	33	31	24.3	22.1	8
52.6	49	47.5	44	42	39	30.8	28.0	9
65	60	58.7	54	52	48	38.0	34.6	10
70.7	73	71.0	66	63	58	46	41.9	11
93.6	87	84.6	78	75	69	54	49.8	12
110	102	99	92	88	82	64.3	58.5	13
127	118	115	107	102	95	74.5	67.8	14
166	154	150	139	133	124	97.4	88.6	16
210	195	190	176	160	156	123.0	112	18
234	217	212	196	188	174	137	125	19
260	241	235	218	208	193	152.0	138	20
314	292	204	263	252	234	184.0	167	22
375	347	338	318	300	278	219.0	199	24
439	407	397	368	352	326	257	234	26

[latex] 34.6\left(\frac{20}{100} ight)(9.81) ext { or } 67.89 N [/latex] (ii).

Step III Force due to acceleration
The mass of the material raised by each wire rope is [latex] \left[\left(\frac{5000}{9.81} ight)\left(\frac{1}{z} ight) ight] [/latex] and that of each wire rope is [latex] \left[34.6\left(\frac{20}{100} ight) ight] [/latex]. The force due to acceleration (i.e., mass × acceleration) is given by,

[latex] \left[\left(\frac{5000}{9.81} ight)\left(\frac{1}{z} ight)+34.6\left(\frac{20}{100} ight) ight](1) [/latex].

or [latex] \left[\frac{509.68}{z}+6.92 ight] N [/latex].

Step IV Number of wire ropes
From Table 23.4, the breaking strength of the wire rope is 48 kN. Assuming the factor of safety to be 10,

[latex] \frac{48000}{10}=\frac{5000}{z}+67.89+\left[\frac{509.68}{z}+6.92 ight] [/latex].

or z = 1.166 or 2 wire ropes.

Question 23.1: A temporary elevator is assembled at the construction site t...

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