Task 2. Determination of geometrical characteristics of plane sections

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 s at each section of the rod and draw diagram N and s to scale.

2. Determine the absolute elongation D 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
			0.4	3.0
			0.5	3.5
			0.6	4.0
			0.7	4.5
			0.8	5.0
			0.9	3.5
			0.35	4.5
			0.45	5.0
			0.55	6.0
			0.65	5.5

Table 2

variant number
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, h ₁ - 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, h 1	Equal angle, mm
		100´6		50´50´3
		120´6		50´50´4
		140´6		50´50´5
		160´6		45´45´5
		180´6		56´56´4
		200´6		56´56´5
		220´6		70´70´5
		240´6		70´70´6
		180´8		56´56´4
		200´8		56´56´5

Fig.4. (see also p.14)

Fig.4. Continued (see also p.15)

Fig.4. Ending

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