# CIVL2112 Structural Analysis- Horizontal Component

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### CIVL2112 Structural analysis

Q1. A plane frame ABCDEFG is hinged supported at A, and is roller supported at B and G, with an internal hinge connection at E, as shown in Figure Q1. It is subjected to a uniformly distributed vertical load of 4 kN/m between C and F, and horizontal loads of 2 kN at H and K.

(i) Find the reactions at supports A, B, and G, and the interaction at hinge E. (6 marks)

(ii) Determine the maximum bending moment in the member CD. (4 marks)

(iii) Draw the bending moment and shear force diagrams for the whole frame, indicating the critical values in the diagrams. Explain why the diagrams are discontinuous at D. State clearly the sign conventions adopted. (15 marks)

Q2. Figure Q2 shows two truss beams are suspended from a parabolic cable DE through a number of closely spaced vertical hangers. The two beams are hinge-connected at C. The beam carries a single load of 50 kN at F. The weights of the beams, the hangers and the cable may be taken to be negligible. Assume that the loads carried by the closely spaced vertical hangers can be represented by an equivalent uniformly distributed load w.

(i) Determine the horizontal component of cable tension, H. (5 marks)

(ii) Determine the value of the uniformly distributed load, w. (10 marks)

(iii) Determine the maximum tension in the cable DE, Tmax. (10 marks)

Q3. A frame ABCDE is pinned supported at A and B, with an internal hinge connection at C, as shown in Figure Q3. All members have the same modulus of elasticity E and second moment of area I. It is acted upon by a uniformly distributed horizontal load q on member AD.

(i) Derive an expression for the horizontal displacement uE at E. (10 marks)

(ii) Derive an expression for the rotation qB at B in radian. (10 marks)

(iii) If H = La = Lb = 6 m, calculate the values of uE and qB. (5 marks)

Q4. (a) The frame shown in Figure Q4(a) is subject to a unit point load P=1 moving on the double layer beam ABCDFGH. Draw the influence lines for the following effects:

(i) Shear force at section 1, Q1 (3 marks)

(ii) Bending moment and Shear force at section 2, M2 and Q2 (6 marks)

(iii) Reaction force at point E, RE (3 marks)

(iv) Shear force at left and right side of point C, QC,L and QC,R (4 marks)

(v) Shear force at left and right side of point F, QF,L and QF,R (4 marks)

(b) Assume that three equally spaced point loads F=10 kN are moving on the double layer beam ABCDFGH, see Figure Q4(b), where the distance between them is d = 1m. Find the maximum positive bending moment and maximum negative bending moment at section 2 under these point loads, M2,max and M2,min, and draw the positions of these point loads for both situations. (5 marks)

### CIVL2112 Structural analysis

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