Question

Figure is an example of a moveable crane on the I-Beam with bolted joint which is located at assembling plant of AliBaba Company. The crane is used to carry and transfer machinery for maintenance purpose. The load from the machinery to be a concentrated loading of 12082 kg. The moveable crane is assumed to be simply supported on the I-Beam with bolted joints. I beam Bolted joint (CONCENTRATED LOADING) 13082 kg Xm 6m BENDING QUESTION: Calculate the thermal expansion in the I-Beam with the temperature range of 45°C (maximum temperature in summer) and -5°C in winter for company at Japan. Is it safe to use this design in Japan? Defend, justify and give reason to your answer. (C35 steel is use for the I-Beam). X-X axis S y-y axis S 1 r r American Standard Channels or C Shapes SI Units Designation Area Depth Web Flange A d thickness Width Thickness tw bf tf mmx kg/m mm2 mm mm W360X 57 7200 358 7.87 172.0 13.1 mm mm 106mm 103 mm3 mm 160 894 149 106mm 11.1 103 mm3 mm 129 39.3

Answer 1

Title - Thermal Expansion

Solution : 0 Given simply supported I- Beam Concentrated loading , W = 12082 kg :: W= 12082 x 9.81 N= 118.5244 X103 N Length of Beam, L= 6 m Material: (35 steel 45°C = -5°C > Maximum temperature , tmax Minimum temperature tmin . Temperature difference, At = tmax - tmin 45-(-5) . 50°C Note : from standard data book, we have that , Young's Modulus of (35 stel, & E= 205 GP a = 205 x 103 m pa and Coefficient of Thermal Expansion, 15 X106/C & Yield strength , Oy = 43ompa STEP 1 : in so now, using the flexural formula , we will find out the strain the extreme fibre due to bending (man strain). Flenural formula, Mmax Ixx omax E R y

FBD, 12082 kg 118.5244 KN AR B с RB 3m 3m K By static Equilibrium , Efx = 0, Efy -o, . RA 118-5244 + RB RA+ RB 118.5244 KN E MA -0, 118.5 244 X 3 RB X 6=0 .. RB 59.2622 KN RA 59.26.22 KN Maximum Bending moment will occur at C, RAX 3 = RB X 3 Mmari Mc Mmax 59.2622x3 = 177.7866 X 10 N-mm

3 Substituting all values in flexural formula, max Simax Ixx 9 omar = M.max.y Ixx max 177.7866 X10' x d/2 Ixx :. Smax 177. 7866 X 10" X 358/2 160 X 100 omax 198.8987 MPa STEP 2: Manimum strain will take place in the extreme flere. E = omax Emax Eman Iman Emax 198.8987 205 X103 Emax = 9.70 23 X 10-4

Now by definition of strain Emax AL L AL Eman .L AL = 9.7023 x10-4 X 6 X109 . AL 5.8213 mm " New de formed length of extreme fibre, .. l=L+AL 6 X103 5.8213 6005-8213mm By formula of Thermal Expansion, Expansion in length change in length due to temperature difference is giren by , ΟΥ Sl = la. AT si 600 5.8213 x 15 x 10-6 x 50 Sl = 4.50 43 mm so the percentage of Thermal expansion is 4.5043 6005.8213 X.100 0.07%

5 While percentage of Expansion due to Bending load and strain caused as , 5.8213 X 100 = 0.09% GOOO Hence as % of expansion due to thermal expansion is less than that compared to the % of expansion due to maximum bending, it is safe to use such a lecam at these diverse temperature regioni - conclusion, it can lee said that I-beam under such temperature circumstancer is absolutely safe to work with in the region of Japan. so as use of I-beam

Summary - First part of the solution consisted of finding the maximum strain through maximum stress. Use of flexural formula was done here. Also the expansion due to bending stress is recorded in the extreme fibre. Second part consist of the expansion in length due to the temperature difference i.e. the thermal expansion. It was concluded that the design is safe for the given atmospheric temperature gradient and location.