A 3-hinged portal frame as shown in Fig. 2.1 is considered. The supports at points A and E are hinged (or pinned). Furth

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A 3 Hinged Portal Frame As Shown In Fig 2 1 Is Considered The Supports At Points A And E Are Hinged Or Pinned Furth 1 (53.37 KiB) Viewed 12 times

A 3 Hinged Portal Frame As Shown In Fig 2 1 Is Considered The Supports At Points A And E Are Hinged Or Pinned Furth 2 (36.37 KiB) Viewed 12 times

A 3 Hinged Portal Frame As Shown In Fig 2 1 Is Considered The Supports At Points A And E Are Hinged Or Pinned Furth 3 (49.98 KiB) Viewed 12 times

A 3-hinged portal frame as shown in Fig. 2.1 is considered. The supports at points A and E are hinged (or pinned). Further, there is a hinge at point C. Due to the fact that there are three hinges, the frame is statically determinate. The moment is zero at the hinges. All the beam parts AB, BC, CD, and DE have the same and constant cross section. The cross section area is A, the shear area is As, the moment of inertia is ly, the modulus of elasticity (or Young's modulus) is E and the shear modulus (or modulus of rigidity) is G. The height of the frame is Hand the span is L. The frame is in general loaded by a horizontal force, P, acting in point B and a vertical uniformly distributed load, q, (units: N/m) acting on the beam parts BC and CD. The load P is a wind load and q is due to self-weight of the structure, snow, and wind. 9 P- B B D B D H L. Do 2L/3 L/3 Fig. 2.1 Geometry, loading, support conditions, and specified positive directions for 3-hinged portal frame
Normal force, shear force, and moment diagrams: Q2.1: Draw the normal force, shear force, and moment diagrams for P acting alone Q2.2: Draw the normal force, shear force, and moment diagrams for acting alone Q2.3: Draw the normal force, shear force, and moment diagrams for P and g acting simultaneously Cross section analysis The cross section of the frame is built up using a steel plate 8x400 mm’and four hollow steel tubes with outer dimensions 100x50 mm", see Fig. 2.2. The cross section area of a tube is Ar = 1810 mm and the moments of inertia about the local principal y-axis and ir axis are lyr = 4.44-10mm' and lot = 0.76-10 mm respectively. а 208 100 8 Ут 50 00V 2 Units: mm Fig. 2.2 Cross section geometry Q2.4: Determine the cross section area, A, and the moment of inertia, ly, about the principal - axis for the cross section shown in Fig. 2.2 Stress analysis: Assume that the frame in Fig. 2.1 has the height H = 5 m, the span L = 10 m and the cross section shown in Fig. 2.2. 6
The steel used for the frame has the same tensile strength, ft, and compression strength, f., i.e. f=f=f- = 250 MPa (= 250 N/mm²). The horizontal load on the frame as shown in Fig. 2.1 is P = 20 kN, q = 8 kN/m. Q2.5: Consider the normal force and moment diagrams in Q2.3. Which points in the frame may be critical when considering the normal stress? Which combinations (N, M) are you going to consider? Q2.6: For all the (N, M)-combinations mentioned in Q2.6 show the normal stress distribution over the cross section for P = 20 kN, q = 8 kN/m(Show the normal stress distribution stemming from the normal force N, show the normal stress distribution stemming from the moment M, and show the resulting normal stress distribution for Nand M acting simultaneously). Software analysis: Q2.7: Use DR FRAME to check your answer to Q2.6. Place the print-outs from your DR FRAME in an appendix called Appendix Q2.7.