SMAT 3 (module)
SHEAR AND MOMENT IN BEAMS
SITUATION.
A simply supported beam AB with a span length of 6 m is loaded
as shown below.
1. Determine the maximum shear.
2. Determine the location of zero shear from A.
3. Determine the maximum moment.
SITUATION.
A concrete pad is shown in the figure. It is supporting thefollowing loads w1 = 290 kN/m
and W2 = 580 kN/m.
4. What is the required length of the pad L so that the upward pressure is uniform?
5. If the shear at 5 meters from the left end is zero, what is the uniform upward pressure in
kN/m?
6. What is the resulting moment at the point of zero shear?
MOVING LOADS
SITUATION.
A truck and trailer combination crossing a 12-m span beam has axle loads of 10 KN, 20 KN,
and 30 kN. The loads are separated by distances of 3 m and 5 m, respectively.
7. What is the distance of the resultant from the 30-kN load?
8. What is the maximum shear developed in the beam?
9. What is the maximum moment developed in the beam?
FLEXURAL STRESS
SITUATION.
The 6-m long cantilever beam made of a T-section Is loaded as shown below.
Section properties:
A = 30,000 mm 2
INA = 345.31 x 106 mm 4
y = 237.5 mm
E = 210 GPa
10. Determine the maximum tensile stress in the beam.
11. Determine the maximum compressive stress in the beam.
12. Determine the corresponding radius of curvature of the beam at the fixed end.
13. Considering the fixed end, determine the total tensile force in the flange.
14. Considering the fixed end, determine the total compressive force in the cross section.
HORIZONTAL SHEAR STRESS
SITUATION.
A rectangular beam 250 mm x 400 mm carries a uniformly distributed load of 10 kN/m over its
simple span of 4 m.
15. Calculate the average shear stress 1 m from the left support.
16. Calculate the shear stress 1 m from the left support at a point 40
mm from the top of the beam.
17. Calculate the maximum shear stress in the beam.
SITUATION.
The I-beam shown below is subjected to a maximum shear of 90 kN, Given the following:
Section properties:
Flange width, br= 250 mm
Flange thickness, tr = 30 mm
Total Depth, d = 380 mm
Web thickness, tw = 25 mm
Moment of inertia, INA = 528.77 × 109 mm 4
18. Determine the average web shear stress.
19. Determine the shear stress at the junction of the flange and web.
20. Determine the maximum shear stress.
21. Determine the percentage of shear carried by the web alone.
SITUATION.
A wooden log is to be used as a footbridge to span a 2.5-m gap. The log is to support a
concentrated load of 30 kN. Neglect the weight of the log.
Allowable shear stress = 1.3 MPa
Allowable bending stress = 7.2 MPa
22. What diameter of the log is needed for maximum shear?
23. What diameter of the log is needed so that the allowable bending stress is not exceeded?
24. A 180-mm wide rectangular log is to be used instead of the circular log. What is the required
minimum depth of the log so as not to exceed the allowable bending stress?