Problem 1:- determine the degree of static indeterminacy of the beam, - dismember the beam elements at the hinge and create the free body diagrams (FBD) of both elements with loading and all external...

Problem 1:- determine the degree of static indeterminacy of the beam,
- dismember the beam elements at the hinge and create the free body diagrams (FBD) of both elements with loading and all external and internal reactions drawn (symbols),
- determine the value of external and internal reactions and create FBD with determined reactions (values) on the separated beam elements and the beam with elements put together,
- check the balance of forces acting on the beam of connected elements.
Problem 2:solve the beam for the internal forces diagrams, according to the instructions written in the form.
Problem 3:determine the cross-section characteristics according to the instructions enclosed in the form.Problem 4:

1. Calculate the depth of the profile according to the attached formula. From the Tables of rolled steel profiles, e.g.https://handysteel.com.au/channels-beams-columns-universal-beams, select the profile (couple of profiles) with the depth closest to the obtained result.
2. Based on the attached formulas, determine the magnitudes of internal forces.
3. Add the sketch of the section to the form.
4. Dimensions, section characteristics, steel symbol and its ultimate strength as well as magnitudes of internal forces write into the tables.
5. Determine characteristic values and draw up stress diagrams.

Additional calculations should be attached on a separate sheet, as attachments.

Problem 1 – Beam Reactions Data: q, l, P= ql, M = ql2 1.167 l1 = l3 = l, l2 = l4 =  l. M1 = ql2 , M2 = ql2 P1 = ql , P2 = ql Free Body Diagram of separated elements (separation at C) - loads and reactions (symbols) Loads and reactions of separated elements (values) Loads and reactions of the beam (values) with connected elements Degree of static indetermination, finding reactions: SN = Checking of the balance of forces (equations of equilibrium of the beam with connected elements): Problem 2 – Internal Forces Known: a, q, P=qa, M =qa2 Free Body Diagram - loads and reactions (symbols) Loads and reactions (values), cross-sections for internal force analysis N qa  qa  qa2 Diagrams of internal forces Degree of static indetermination, finding reactions: Schemes for analysis of internal forces: Functions of internal forces: At least 3 result verifications: boundary conditions, T or M jumps at sections of force or moment application, max M (x) at sections where T =0, etc.: Problem 3 - moments of inertia Known: a Mark on the figure: centroid, centroidal axes Cx1C, Cx2C and principal axes Cx1p, Cx2p through centroid Cross-sectional area: A = Static moment with respect to Ox1: Sx1 = Static moment with respect to Ox2: Sx2 = Coordinates of centroid: x1C = x2C = C (x1C, x2C) = Moments of inertia with respect to Ox1, Ox2: Jx1 = Jx2 = Jx1x2 = Moments of inertia with respect to Cx1C, Cx2C: Jx1C = Jx2C = Jx1Cx2C = Mohr’s circle: r = 0 = JC = J1 = J2 = Problem 4 – Stress Analysis Cross-section Shear stress [MPa] Normal stress [MPa]  g r/sc  = g + r/sc (mark the position of centroid) T M N Internal forces bending tension/compression total normal stress 1. Determination of the rolled cross-section depth m = 6 , n = 7 ,  =0.86 , h = 100  = 86 Chosen cross-section depth (as the nearest to calculated h): ……………….. Dimensions and characteristics of the profile (the sketch of your cross-section draw in the table above) h s b t x2C A Jx3C W3 [mm] [cm2] [cm4] [cm3] b x2C x3C C s hs t b t x2C x3C C s hs t b t x2C x3C C b x2C x3C C s hs t 2. The cross-section load capacity 3. Internal forces Symbol stali kd Mmax N T M [MPa] [MPa] [kN] [kN] [kNcm] Allowable stress (tension/compression) kd [MPa], bending moment M =0,3 (-1)n+m W3 kd [kNcm], normal force N=0,4 (-1)nA kd [kN] , shear force: T =0,5(-1)m N [kN] . Attach calculations of the cross-section load capacity in the case of pure bending (Mmax-?), as well as for complex loading, NTM,calculations of normal stress max, min, r/c ,maxr/c, maxr/c and shear stress  C , K , K’ , across the given cross-section. Calculations should be done with the use of units [kN] and [cm], result obtained in [kN/m2] should be converted into [MPa]. a a a 2a a a x 2 x 1 O