参见附件，有模型有算例有理论解。欢迎指正。解压缩后为pdf格式。
按说瑞利解的频率应该比理论解略高才对，现在有点低，原因不详。不过精度还是不错的。

MODAL CALCULATION REQUESTED 这个命令的算例。

楼上说的很好，但感觉有关特征值工况的“质量建模”部分有可能误导读者，因此这里在补充一些资料，特别注意最后一段内容（完整该内容见附件文档）：

The MASSES which are to be used in assembling the MASS MATRIX

The mathematical method that STAAD uses is called the subspace iteration eigen extraction method. Some information on this is available in Section 1.18.3 of the STAAD.Pro Technical Reference Manual. The method involves 2 matrices - the stiffness matrix, and the mass matrix.

The stiffness matrix, usually called the [K] matrix, is assembled using data such as member and element lengths, member and element properties, modulus of elasticity, poisson's ratio, member and element releases, member offsets, support information, etc.

For assembling the mass matrix, called the [M] matrix, STAAD uses the load data specified in the load case in which the MODAL CAL REQ command is specified. So, some of the important aspects to bear in mind are:
The input you specify is weights, not masses. Internally, STAAD will convert weights to masses by dividing the input by "g", the acceleration due to gravity.

If the structure is declared as a PLANE frame, there are 2 possible directions of vibration - global X, and global Y. If the structure is declared as a SPACE frame, there are 3 possible directions - global X, global Y and global Z. However, this does not guarantee that STAAD will automatically consider the masses for vibration in all the available directions.

You have control over and are responsible for specifying the directions in which the masses ought to vibrate. In other words, if a weight if not specified along a certain direction, the corresponding degrees of freedom (such as for example, global Z at node 34) will not receive a contribution in the mass matrix. The mass matrix is assembled using only the masses from the weights and directions specified by the user.

In our example, notice that we are specifying the selfweight along global X, Y and Z directions. Similarly, the element pressure load is also specified along all 3 directions. We have chosen not to restrict any direction for this problem. If a user wishes to restrict a certain weight to certain directions only, all he/she has to do is not provide the directions in which those weights cannot vibrate in.

As much as possible, provide absolute values for the weights. STAAD is programmed to algebraically add the weights at nodes. So, if some weights are specified as positive numbers, and others as negative, the total weight at a given node is the algebraic summation of all the weights in the global directions at that node.（这里强调在特征值分析工况的“荷载”一定要输入绝对值！如果有正有负的话，STAAD会进行代数叠加，这样，就会遗漏一部分质量，切记！）

可否把这些重要说明加入到帮助文件中啊。

帮助文件1.18.3.2也提到了很多。
例如，其中有句话：
“ Please enter selfweight, joint and element loadings in global directions with the same sign as much as possible so that the “masses” do not cancel each other ”

以下算例中，“6 FY -100” 和“6 FY 100”，所求的振型结果没有差别啊。 V8i中，求解振型时，可以无视荷载正负号了？

STAAD SPACE
UNIT METER KN
JOINT COORDINATES
1 0 0 0 11 10 0 0
MEMBER INCIDENCES
100 1 2  109 1 1
*********************
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+008
POISSON 0.3
DENSITY 78.49
ALPHA 1.2e-005
DAMP 0.03
END DEFINE MATERIAL
*********************
MEMBER PROPERTY CHINESE
100 TO 109 PRIS YD 0.4 ZD 0.3
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED BUT FX MY MZ
11 PINNED
*****************************
LOAD 1 DEAD AND LIVE LOAD
SELFWEIGHT X 1
SELFWEIGHT Y 1
SELFWEIGHT Z 1
JOINT LOAD
6 FY -100
*6 FY 100

MODAL CALCULATION  
PERFORM ANALYSIS
FINISH

我用楼上的算例做了些修改，分别在5和7号节点加-100KN的竖向荷载，然后进行分组，分四次。
第一次：节点5 -100KN 节点7 -100KN
第二次：节点5 100KN  节点7 -100KN
第三次：节点5 100KN 节点7 100KN
第四次：节点5 -100KN 节点7 100KN
四次运算的结果一样，说明07版STAAD PRO V8I在加与质量相关的荷载时，程序会自动按绝对值处理。
算例如下：
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 16-Aug-11
END JOB INFORMATION
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 1 0 0; 3 2 0 0; 4 3 0 0; 5 4 0 0; 6 5 0 0; 7 6 0 0; 8 7 0 0;
9 8 0 0; 10 9 0 0; 11 10 0 0;
MEMBER INCIDENCES
100 1 2; 101 2 3; 102 3 4; 103 4 5; 104 5 6; 105 6 7; 106 7 8; 107 8 9;
108 9 10; 109 10 11;
*********************
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+008
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-005
DAMP 0.03
G 7.88462e+007
TYPE STEEL
STRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2
END DEFINE MATERIAL
*********************
MEMBER PROPERTY CHINESE
100 TO 109 PRIS YD 0.4 ZD 0.3
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED BUT FX MY MZ
11 PINNED
*****************************
LOAD 2 LOADTYPE None  TITLE LOAD CASE 2
SELFWEIGHT X -1 LIST 100 TO 109
SELFWEIGHT Y -1 LIST 100 TO 109
SELFWEIGHT Z -1 LIST 100 TO 109
JOINT LOAD
5 FY -100
7 FY 100
MODAL CALCULATION REQUESTED
PERFORM ANALYSIS
FINISH

質量的輸入都用正值或都用負值，結果可能是一樣的。樓上算例已經證實。
但如果一部份質量用正值，另一部份用負值，就會引起質量的部份抵消。前面貼出的文件，重點是說這個問題。

模态分析中的质量都用正值

在反应谱分析时可以输入负的质量了（V8i 20.07.04.12）。另外，在定义地震荷载（底部剪力）中，也可以输入+Y方向的力（相当于负的质量）。程序求解时会扣除这部分负的质量。前两天在研究印度抗震规范时还专门建模进行测试验证过。