316 PRACTICAL MATHEMATICS 



length and draw the bending moment diagram. What is the 

 maximum bending moment and where does it occur ? 



(4) A beam 30 ft. long is supported at the ends A and B ; C is a 

 point 10 ft. from A. The part AC of the beam is unloaded, while 

 the part BC carries a load which increases uniformly from at C 

 to 2 tons at B. Find expressions for the bending moment for the 

 two parts of the beam and draw the bending moment diagram. 

 What is the maximum bending moment and where does it occur ? 



(5) A beam 30 ft. long is supported at the ends A and B ; C is a 

 point 12 ft. from A. The part AC carries a uniformly distributed 

 load of 1^ tons per foot run, while the part CB carries a load which 

 decreases uniformly from 1-| tons at C to at B. Find expres- 

 sions for the bending moment for the two parts of the beam and 

 draw the bending moment diagram. What is the maximum 

 bending moment and where does it occur ? 



(6) A cantilever of length I ft. is loaded at the free end with 

 W tons ; it also carries a uniformly distributed load of w tons per 

 foot run. Find the bending moment, the slope and the deflection 

 at a point P, which is situated at a distance x ft. from the point 

 of fixing. What is the deflection at the free end ? 



(7) A beam of length 2a ft. is supported at the ends and is 

 loaded with W tons at the centre ; it also carries a uniformly dis- 

 tributed load of w tons per foot run. P is a point situated at a 

 distance x ft. from the centre of the beam. Find the bending 

 moment, the slope, and the deflection at P. 



(8) A beam of length 2 ft. is fixed at both ends and is loaded 

 with W tons at the centre ; it also carries a uniformly distributed 

 load of w tons per foot run. Find the magnitude of the fixing 

 couple. If P is a point situated at a distance x ft. from the centre 

 of the beam, find the bending moment, the slope, and the deflec- 

 tion at P. For what value of x is the bending moment zero ? 



(9) A cantilever of length I ft. carries a load which decreases 

 uniformly from w tons at the fixed end to. at the free end. 

 Find the bending moment, the slope, and the deflection at a 

 point situated at a distance x ft. from the fixed end. What is 

 the maximum deflection ? 



(10) A beam of length 2a ft. is supported at the ends and 

 carries a load which decreases uniformly from w tons at the centre 

 to at the ends. Find the bending moment, the slope, and the 

 deflection at a point which is situated at a distance x ft. from 

 the centre. What is the maximum deflection ? 



(11) A beam of length 2a ft. is fixed at the ends and carries a 

 load which decreases uniformly from w tons at the centre to at 

 the ends. Find the magnitude of the fixing couple. If P is a 

 point situated at a distance x ft. from the centre, find the bend- 

 ing moment, the slope, and the deflection at P. What is the 

 bending moment at the end ? 



