Moving load

Moving load (Mechanics of Solid)

1. Mechanics of Solids-I UE-251 Teacher :Sadaqat khan Group Member Abdul Hai UE-19038 Nasir Hussain Sani UE-19027 Ammar Ali UE-19034 Effect of Abdul Hai

2. Moving Load We know that The maximum moment occurs at a point of zero shears. For beams loaded with concentrated loads, the point of zero shears usually occurs under a concentrated load and so the maximum moment. Beams and girders such as in a bridge or an overhead crane are subject to moving concentrated loads, which are at fixed distance with each other. The problem here is to determine the moment under each load when each load is in a position to cause a maximum moment. The largest value of these moments governs the design of the beam. Effect of Abdul Hai

3. Single Moving Load For a single moving load, the maximum moment occurs when the load is at the midspan and the maximum shear occurs when the load is very near the support (usually assumed to lie over the support). M max = PL V max = P 4 Effect of Abdul Hai

4. TWO MOVING LOADS For two moving loads, the maximum shear occurs at the reaction when the larger load is over that support The max moment is given as above Where Ps is the smaller load, Pb is the bigger load, and P is the total load (P = Ps + Pb). M max =( PL − Psd ) 4 PL 2 Effect of Abdul Hai

5. Three moving load In general, the bending moment under a particular load is a maximum when the center of the beam is midway between that load and the resultant of all the loads then on the span. With this rule, we compute the maximum moment under each load, and use the biggest of the moments for the design. Usually, the biggest of these moments occurs under the biggest load. The maximum shear occurs at the reaction where the resultant load is nearest. Usually, it happens if the biggest load is over that support and as many a possible of the remaining loads are still on the span. In determining the largest moment and shear, it is sometimes necessary to check the condition when the bigger loads are on the span and the rest of the smaller loads are outside. Effect of Abdul Hai

6. Numerical Three wheel loads roll as a unit across a 44-ft span. The loads are P 1  = 4000 lb and P 2  = 8000 lb separated by 9 ft, and P 3  = 6000 lb at 18 ft from P 2 . Determine the maximum moment and maximum shear in the simply supported span. Solution: R=P1+P2+P3 R=4000+8000+6000 R =18,000lbs (x)R=9P 2 +(9+18)P 3 x(18)=9(8)+(9+18)(6) x=13ft the resultant R is 13 ft from P 1 Maximum moment under P 1 Σ M R 2 =0 44R 1 =15.5R 44R 1 =15.5(18) R 1 =6.34091kips R 1 =6,340.91lbs Effect of Abdul Hai

7. M TotheleftofP 1 =15.5 R 1 M TotheleftofP 1 =15.5(6340.91) M TotheleftofP 1 =98,284.1lb⋅ft Maximum moment under P 2 Σ M R 2 =0 44 R 1 =20 R 44 R 1 =20(18) R 1 =8.18182kips R 1 =8,181.82lbs M TotheleftofP 2 =20 R 1−9 P 1 M TotheleftofP 2 =20(8181.82)−9(4000) M TotheleftofP 2 =127,636.4lb⋅ft Maximum moment under P 3 Σ R 1 =0 44 R 2 =15 R 44 R 2 =15(18) R 2 =6.13636kips R 2 =6,136.36lbs Effect of Abdul Hai

8. M TotherightofP 3 =15 R 2 M TotherightofP 3 =15(6,136.36) M totherightofP 3 =92,045.4lb⋅ft Thus, M (max) = MTotheleftofP 2 M (max) =127,636.4lb⋅ft The maximum shear will occur when P 1  is over the support. Σ M R 2 =0 44 R 1 =31 R 44 R 1 =31(18) R 1 =12.6818kips R 1 =12,681.8lbs Thus, Vmax =12,681.8lbs Effect of Abdul Hai

9. Numerical A truck with axle loads of 40 kN and 60 kN on a wheel base of 5 m rolls across a 10-m span. Compute the maximum bending moment and the maximum shearing force. Solution: R =40+60=100kN xR =40(5 ) x =200/ R x =200/100 x =2m For maximum moment under 40 kN wheel: Σ MR 2=0 10 R 1=3.5(100) R 1=35k MTotheleftof 40 kN =3.5 R 1 MTotheleftof 40 kN =3.5(35) MTotheleftof 40 kN =122.5kN⋅m Effect of Abdul Hai

10. For maximum moment under 60 kN wheel: Σ M R 1 =0 10R 2 =4(100) R2=40kN M Totherightof60kN =4 R 2 M Totherightof60kN =4(40) M Totherightof60kN =160kN⋅m Thus, M max =160kN⋅m The maximum shear will occur when the 60 kN is over a support. Σ M R 1 =0 10R 2 =100(8) R 2 =80kN Thus, V max =80kN Effect of Abdul Hai

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