ADVANCED STRENGTH OF MATERIALS UNIT :2

UNIT : 2
Indeterminate Beams
1. What do you mean by propped cantilevers?
Propped cantilevers means cantilevers supported on a vertical supported at a
suitable point.
2. How will you find the reaction at the prop?
The reaction of the prop is calculated by equating the down ward deflection due to
load at the point of prop to the upward deflection due in prop reaction.
3. What do you mean by a fixed beam?
A beam whose both ends are fixed is known as fixed beam.
4. What do you mean by a continuous beam?
A beam which is supported on more than two supports is known as a continuous
beam.
5. What is the advantage of fixed beam:
a. The beam is more stable and stronger
b. The slope at both ends of a fixed beam is Zero
c. The fixed beam is subjected to a lesser maximum bending moment
d. The maximum deflection of a fixed beam is less than that of a simply supported
beam.
6. Find an expression for the deflection for a fixed beam carrying a udl throughout the span.
Y=wl^4/192EI
7. Find an expression for deflection for a fixed beam carrying a point load at the centre.
Y=wl^4/384EI

8. State theorem of three moments.
MAL1 + 2MB (L1 + L2) + MC L2 = -6(a1x1/L1 +a2 x2/L2)
A1 = Area of BM diagram due to Vertical loads on Span AB
A2 = Area of BM diagram due to Vertical loads on Span BC
X1= Distance of C.G. of BM diagram due to Vertical load on AB from A
X2= Distance of C.G. of BM diagram due to Vertical load on BC from point C
9. How will you apply clapeyron’s theorem of three moments to a continuous beam with
simply supported ends.
MAL1 + 2MB (L1 + L2) + MC L2 = -6( a1x1/L1 +a2 x2/L2)
The fixing moments on the ends of a simply supported beam is Zero.
MA = MC = 0
10. What is the reaction for a cantilever carrying a udl over the entire span and propped
rigidly at the free end,
P = 3/8 WL
11. Find the BM at fixed end for a cantilever carrying a udl over the entire span and propped
rigidly at the free end.
M= WL^2/8
12. Find the deflection at the centre for a cantilever carrying a udl over the entire span and
propped rigidly at the free end.
Y C= WL^4/192EI
13. What is the prop reaction for a simply supported beam, carrying a udl over the entire span
and propped at the centre.
P = 5/8W
14. Find the support reaction for a simply supported beam, carrying a udl over the entire span
and propped at the centre.
RA = RB = 3W/16
15. Find the B.M at centre for a simply supported beam, carrying a udl over the entire span
and propped at the centre.
M = -WL^2/32
16. Find the deflection for a simply supported beam, carrying a uniformly distributed load
over the entire span and propped at the centre.
Y = WL^4/384EI