Tối ưu hóa các mặt cắt ngang hình tam giác để tăng khả năng chịu tải của thanh dầm chữ i

Journal of Science & Technology 100 (2014) 006-010

Optimizing Triangular Cross Section

for Increasing Load Capability of I-Beam

Trinh Dong Tinh*, Vuong Van Thanh Hanoi University ofScience and Technology, No. 1, Dai Co Viet Str., Hai Ba Trung, Ha Noi, Viet Nam

Received: December 27, 2013; accepted- April 22, 2014

Abstract

Results of analysis on load capability of I-beam using as a railway of hoist in single girder crane show that

the standard I-beam is applicable only for the crane with shoii span and tight capacity. This paper

presents a combined beam, make of I-beam and steel plate to change the cross section to triangular type

with goal increasing the load capability of the beam, loaded in both vertical and horizontal directions, and

improves the torsion resistance as well. The dimensions of the combined beam are determined by

establishing and solving the structure optimizing problem with the goal to minimize the beam's weight in

the terms of strength, stiffness and technology of the structure. The globalized reduced gradient method,

integrated in Excels as Solver tool is used to solve this nonlinear optimization problem.

Keywords: Crane metal stnjcture, I-beam, Cross-section optimization

1. Introduction

The steel I-beam is widely applied as the main

beam in the cranes and the portal bridge crane.

Besides, it is also used in the monorail systems for

mechanical handling of materials in workshops and

storages. For these machines, the electtic hoists are

usually used as equipment for lifting, lowering the

load and transporting it along the I-beam as shown in

Fig,I [i].

The rated load (load capacity) and other

parameters of electric hoist are standardized by the

hoist manufacture and for each series of rated load

the hoist manufacture also specified which size of

standard I-beam to use with. For example, with the

V-series electric hoist, lifting height ranges from 6 to

8 m, the main parameters of hoist and I-beam are

listed in Table I.

When the mechanisms work, the loads acting

on the beam include the lifting load, the weight of

hoist, and the dynamic loads. These loads cause the

stiess in the beam and deform it. In order to guarantee

the work ability of stmcture, the maximum stress and

the deformation must be less than the allowable

values.

The sttess and deformation of the main beam

of overhead travelling crane could be calculated by

using the diagram shown in Fig.2 [2], in which:

S is considered as concenttated load, including the

lifting load SL, the weight of electric hoist Sec and the

'Corresponding author, Tel, (+84) 904.274.984

Email [email protected] vn

dynamic vertical loads;

dts the disttibuted load caused of the beam's weight;

Sfi and dH are the horizontal loads by the inertial force

on the main beam when the crane starts or stops. In

the case of common cranes, horizontal load is taken

by 10% of vertical loads;

L is the span of the main beam, and

X is the location of electric hoist on the beam, and

varies from 0 to L.

The sttess and deflection will be maximum at

the center of beam when the hoist is at this place (JC -

L/2). The effect of beam's weight is not large [3, 4],

and it can be ignored in preliminary calculation.

In order to satisfy the requirement on the

strength, the maximum sttess should satisfy:

(T = ^ z + -^y<{a\ (I)

Where My and Mz are the bending moment fo

the y and z axis, respectively.

When ignoring beam's weight, these values

are calculated by the following equations:

M^^^ ; M.=^^ (2)

^ 4 ' 4 ^

ly and h are the moment of inertia of the cross section

with respect to the y, z axis, respectively.

y and z are the coordinates of the points on the cross

section,

[a] is the allowable sttess of beam material, equal to

the ratio of the yield stiess and the safety factor.