Question

A crane is a type of machine mainly used to lift, lower, and horizontally move heavy objects. It is immensely useful in construction works. In this problem, we will be analyzing a type of crane called a luffing crane. Cable Gantry 20 m 6 m 30 10000 N 30- Jib 10 m 20000 N Main mast Figure 1: a typical laffing crane As illustrated in fig. 1.a luffing crane typically consists of a main mast, a jib, a gantry and a counterweight. The jib and the gantry are always perpendicular, but the jib can vary in angle with the horizontal line. In this problem, however, we will consider it fixed at 30. The counterweight is palling directly downward on the end of the gantry, which is also connected to the end of the jib by a cable. In reality, the main mast and jib are made of multiple short columns and beams welded together into a compound structure. For this problem, however, we will assume that the mast and jib are each made of a single constant cross-section steel. The steel has E 210 GPa, S, 400 MPa, and S -550 MPa In this problem, the main mast is 10 m long, the jib is 20 m long, and the gantry is 6 m long. The counterweight weighs 20000 N. The angle 30. The maximum weight that the crane can lift is 10000 N. The safety factors of the mast and the jib are 2 and 3, respectively. The jib can be considered fixed to the mast, while the mast base is fixed to the ground and free to move at the top. Determine the required section modulus Zat and Zb and moments of inertia ar and Ib of the mast and the jib. Ignore fatigue and stress concentration factors. You may assume that the mast, jib, and gantry are weightless

Answer 1

ASSumption: The most ond Jib ore mode of Sivale conehkont cireulor cross-seetion Sheek of diameter dlt ond die res Reekives FBD of Jib -30° 60 20 M 6A 30 Arial compressive force on Jib 10,000 Cas6o 5000N perpendieular force 8660.25 N Per miss ible stresses Slas Sy (Sut ais 400 133.33MPA 3 Sut 183.33 MPa. (Sutlela FeomP 5000 TT Area 5 000 Or1 183.33 7Td 2 .d - 5.896 mm

Moment due o fer pendieulor force, MJre8660. 25(2010)ne N-Mm - Ajt o 33.205 10 from Bendiva er Muik 1/4 0000 L 173-205 N-mm 132-33 OV 1 ib 43K10 mM (Ant) I b4 as 0338 2250:2 13-2440 23 6-58 mm 237mm out of these two d values Freater and safe for ule. Hen ce JJib 287mm is 154.87K10 64 Ans)

Considering design of Matt 20 .5σ00 Ν 2000ON 10000 M 30 veCf forces from antry ko mast 20000Sinso9OU000 2σσυ eo 1Henee eompreesive force or Most hed 19320.5K eaS305000 Sin30 M3 1500 N Permissible stress 400 = 200 MPaj 2 lalw (Sutblaw 550 25 MPa 2 or, d 9.00 mmm Conder ing bending t hed of mast EM; (40000 A 20cos 30) ( 200 κοω έc) o000 CoS 113 205-1 113 205 1D Nmm

M MOODD tMast 113. 205O Of, 200 1 7mast SL6.025O Emast Imalt 3 TT 3 2 49-3 180 mm 2. d Sk onsilerig bending a oale +DEM 5000 cos8010) -(7520.5ima 48301.23 N-m zin (S das 433 01-2310 Tmast そmagt-- 216-5103 mm 265103 32 dM120. 2. 121mm Out of these d value 180mm is a reater and Safe for e Henee Imast s 5J.53 40 mm