Beam Deflection

Situation
A simply supported beam has a span of 12 m. The beam carries a total uniformly distributed load of 21.5 kN/m.
1.   To prevent excessive deflection, a support is added at midspan. Calculate the resulting moment (kN·m) at the added support.

2.   Calculate the resulting maximum positive moment (kN·m) when a support is added at midspan.

3.   Calculate the reaction (kN) at the added support.

Situation
A cantilever beam, 3.5 m long, carries a concentrated load, P, at mid-length.

1.   How much is the deflection (mm) at mid-length?

2.   What force (kN) should be applied at the free end to prevent deflection?

3.   To limit the deflection at mid-length to 9.5 mm, how much force (kN) should be applied at the free end?

Situation
A simply supported steel beam spans 9 m. It carries a uniformly distributed load of 10 kN/m, beam weight already included.

1.   What is the maximum flexural stress (MPa) in the beam?

2.   To prevent excessive deflection, the beam is propped at midspan using a pipe column. Find the resulting axial stress (MPa) in the column

3.   How much is the maximum bending stress (MPa) in the propped beam?

Situation
A beam of uniform cross section whose flexural rigidity EI = 2.8 × 10¹¹ N·mm², is placed on three supports as shown. Support B is at small gap Δ so that the moment at B is zero.
 

1.   Calculate the reaction at A.

2.   What is the reaction at B?

3.   Find the value of Δ.