Task 1. Analysis of stepped rod in tension-compression

The stepped rod (fig. 1) is under the action of longitudinal axial forces F and distributed load q. To carry out the analysis of the rod.

Take the data for computation from table 1 and material mark from table 2. accept the safety factor as following:

- for ductile materials n_y = 1,5; for brittle materials n_s = 2,5

Order of work

1. Using the method of the section determine the normal axial force N and normal stress  at each section of the rod and draw diagram N and  to scale.

2. Determine the absolute elongation l of each section and draw the diagram of the cross-section motion along the rod.

3. Calculate allowable values of stress, determine the dangerous section of the rod and make the conclusion about strength of the rod.

Table 1

variant number / group No. /	Loading		Length a , m	Area A, cm 2
	F, kN	q , kN/м
201	20	12	0.4	3.0
202	22	10	0.5	3.5
203	24	16	0.6	4.0
204	26	14	0.7	4.5
205	28	20	0.8	5.0
206	21	11	0.9	3.5
207	23	15	0.35	4.5
208	25	13	0.45	5.0
209	27	19	0.55	6.0
210	29	17	0.65	5.5

Table 2

variant number	1	2	3	4	5	6	7	8	9	10
Material	30ХГСА	45Х	Ст 3	30Г	Д6	СЧ38-60	20Х	12ХН3А	Д1П	20Г

Fig.1. (see also p.5)

Fig.1. Continued (see also p.6)

Fig.1. Ending

Task 2. Determination of geometrical characteristics of plane sections

Determine values of the principal centroidal moments of inertia and position of the principal centroidal axes of compound section (fig. 4).

Take the data necessary for computation from table 4.

Order of work

1. Draw the section to scale and mark the dimensions; h – I-siction height, h₁ - height of channel, b - width, t - thickness of the stripe.

2. Determine the centroid of the section with respect to selected auxiliary axes. Draw centroidal axes.

3. Determine values of moments of inertia: axial moment I_x and I_y , and product of inertia (centrifugal moment)I_xy respecting central axes.

4. Determine the position of principal centroidal axes of inertia u and v and show them on the sectional drawing.

5. Determine values of the principal moments of inertia I_u and I_v.

6. Make necessary checks for I_yc + I_zc = I_u + I_v; I_uv = 0.

table 4

variant number /group No./	I-section number, h	Stripe bt, mm	Channel number, h1	Equal angle, mm
201	10	1006	16	50503
202	12	1206	16	50504
203	14	1406	18	50505
204	16	1606	18	45455
205	18	1806	20	56564
206	12	2006	20	56565
207	14	2206	22	70705
208	16	2406	22	70706
209	20	1808	24	56564
210	18	2008	24	56565

Fig.4. (see also p.14)

F ig.4. Continued (see also p.15)

F ig.4. Ending