Advanced Methods of Structural Analysis

4.4 Nil Point Method for Construction of Influence Lines 95 Location of NP.Mk/may be computed by formula uMD lf xk ykl 2 Cxkf : ...

96 4 Three-Hinged Arches Step 2.Lay off along the vertical passing through the supportA, the value cos'k. Step 3.Connect this or ...

4.5 Special Types of Arches 97 * sinjk − NP(Nk) A C B 1 3 5 2 k 7 6 P= 1 NP(Nk) Tangent at k Perpendicular to tangent at k LHP R ...

98 4 Three-Hinged Arches where span for archACB^0 with support points on the same level isLD lCl 0 D 48 m. ForxD 42 m (support ...

4.5 Special Types of Arches 99 The total vertical reactions may be defined as follows RADR^0 ACZsin ̨D2:857C11:4680:08304D3:809 ...

100 4 Three-Hinged Arches Inf. line H + 1.1428 1.71428 Inf. line Mk (m) xk=6m + x 0 = 16.8m − 2.5714 1.7143 8m C B A P=10kN H H ...

4.5 Special Types of Arches 101 y 1 x 1 q=2kN/m H H D A′ B′ 12m RA RB E F HA B A C f=12m Parabolic arch f 0 =2m ak=18m l=48m k F ...

102 4 Three-Hinged Arches Note, that the discontinuity of the shear and normal forces at section E left and right at the vertica ...

Problems 103 Inf. line H 1.2 + 0.6 Inf. line MK (m) 11.25–8.325 =2.925 NP(MK) 11.1–9.0=2.1 + − 1.05 y x yk= 11.25m 1 1 H H A′ B′ ...

104 4 Three-Hinged Arches A C B 1 2 3 n P= 1 bc k ac fc Fig. P4.2 4.3.Design diagram of three-hinged arch is presented in Fig.P4 ...

Problems 105 4.Decreasing of external temperature within the left half-archACleads to appear- ance of internal forces at at the ...

106 4 Three-Hinged Arches 4.7.Three-hinged askew arch spanlis subjected to concentrated forcePat the hingeC(Fig.P4.7). Determine ...

Problems 107 4.10.Three-hinged symmetrical arch is loaded by distributed loadqas shown in Fig.P4.10. Find equation of the ration ...

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Chapter 5 Cables This chapter is devoted to analysis of cables under fixed loads of different types. Among them are concentrated ...

110 5Cables a Anchor span Anchorage Pillar Hangers Main span Sag Fig. 5.1 Suspension bridge Another feature of cables is the hig ...

5.1 Preliminary Remarks 111 for practice this type of problem does nothave a reasonable sense because shape of the cable cannot ...

112 5Cables denoted asrAandhAfor supportAandrBandhBfor supportB. Summing of all forces on the horizontal axis leads to the relat ...

5.2 Cable with Neglected Self-Weight 113 The concept of “shear” at the any section of the reference beam will be helpful. The po ...

114 5Cables RA H NA- 1 A k k RA H NA- 1 b c P=20kN A B 120kNm C a P=20kN RA x H RB H y a=10m l=25m a 1 a 0 a 0 a 0 A B 1 f k k b ...